Maths-
General
Easy

Question

For Christmas, Maryland purchased subscriptions to Xbox Live for her four children. Each subscription costs $5 per month plus a $15 sign-up fee. If she received a bill for $120, for how many months did she purchase subscriptions for her children?

The correct answer is: x = 3


    • Hint:
    ○ Form the eqaution using given information.
    ○ Take variable value as any alphabet.
    ○ Take terms with cofficient at one side and without cofficients at another side.
    • Step by step explanation:
    ○ Given:
    Sign up fee per subscription = $15.
    Subscription cost per month = $5.
    Total subscription purchased = 4
    Total bill = $120.
    ○ Step 1:
    Let Maryland purchase membership for x months.
    So,
    Bill  for 1 month for 1 child  = sign up fee + monthly cost
    Bill  for 1 month for 1 child  =  15 + 5
    Bill  for x month for 1 child  =  15 + 5x
    Hence,
    Bill  for x month for 4 child  = ( 15 + 5x )  4
    Bill  for x month for 4 child  = ( 60 + 20x )
    ○ Step 2:
    ○ As total bill is $120.
    ∴ 60 + 20x = 120
    rightwards double arrow20x =  120 - 60
    rightwards double arrow20x = 60
    rightwards double arrowx = 60 over 20
    rightwards double arrowx = 3
    • Final Answer:
    Hence, Maryland purchase 3 month subscription for childen.

    Related Questions to study

    General
    Maths-

    State the law of logic that is illustrated.
    If 𝑥 + 2 = 4, then 𝑥 = 2.
    If 𝑥 = 2, then 𝑥2  = 4.
    If 𝑥+2=4, then 𝑥2 = 4

    Hint:
    Law of Syllogism states that:
    Law of Syllogism states that:
    1) if p not stretchy rightwards arrow q is true
    2) If q not stretchy rightwards arrow r is true
    then we can conclude that p  r is also true.
    Solution
    It is given that: If 𝑥 + 2 = 4, then 𝑥 = 2, If 𝑥 = 2, then 𝑥2  = 4 and If 𝑥+2=4, then 𝑥2=4. So if we take
    p: 𝑥 + 2 = 4
    q: 𝑥 = 2
    r: 𝑥2  = 4
    So can write the given statement “If 𝑥 + 2 = 4, then 𝑥 = 2” as p  q and the statement “If 𝑥 = 2, then 𝑥2  = 4” can be written as q  r and also the statement “If 𝑥+2=4, then 𝑥2 = 4” can be written as p  r.
    So we can see that we are given: p not stretchy rightwards arrow  q is true
    not stretchy rightwards arrow  r is true
    not stretchy rightwards arrow  r is true
    This statement resolves the law of syllogism which states that if p not stretchy rightwards arrow q is true and If q not stretchy rightwards arrow  r is true then we can conclude that p  r is also true
    Final Answer:
    Hence, the law of logic which is used in these statements is the law of syllogism

    State the law of logic that is illustrated.
    If 𝑥 + 2 = 4, then 𝑥 = 2.
    If 𝑥 = 2, then 𝑥2  = 4.
    If 𝑥+2=4, then 𝑥2 = 4

    Maths-General
    Hint:
    Law of Syllogism states that:
    Law of Syllogism states that:
    1) if p not stretchy rightwards arrow q is true
    2) If q not stretchy rightwards arrow r is true
    then we can conclude that p  r is also true.
    Solution
    It is given that: If 𝑥 + 2 = 4, then 𝑥 = 2, If 𝑥 = 2, then 𝑥2  = 4 and If 𝑥+2=4, then 𝑥2=4. So if we take
    p: 𝑥 + 2 = 4
    q: 𝑥 = 2
    r: 𝑥2  = 4
    So can write the given statement “If 𝑥 + 2 = 4, then 𝑥 = 2” as p  q and the statement “If 𝑥 = 2, then 𝑥2  = 4” can be written as q  r and also the statement “If 𝑥+2=4, then 𝑥2 = 4” can be written as p  r.
    So we can see that we are given: p not stretchy rightwards arrow  q is true
    not stretchy rightwards arrow  r is true
    not stretchy rightwards arrow  r is true
    This statement resolves the law of syllogism which states that if p not stretchy rightwards arrow q is true and If q not stretchy rightwards arrow  r is true then we can conclude that p  r is also true
    Final Answer:
    Hence, the law of logic which is used in these statements is the law of syllogism
    General
    Maths-

    Show the conjecture is false by finding a counterexample. If A, B and C are collinear, then AB + BC = AC.

    Hint:
    Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.
    Counterexample: It is an example which shows that the conjecture is false.
    Solution


    In the given figure points A, B and C are collinear.
    But here AC + CB = AB instead of  AB + BC = AC. So the given conjecture is wrong.
    Final Answer:
    Hence, the counterexample for the given example i.e. “If A, B and C are collinear, then AB + BC = AC” is the above diagram.

    Show the conjecture is false by finding a counterexample. If A, B and C are collinear, then AB + BC = AC.

    Maths-General
    Hint:
    Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.
    Counterexample: It is an example which shows that the conjecture is false.
    Solution


    In the given figure points A, B and C are collinear.
    But here AC + CB = AB instead of  AB + BC = AC. So the given conjecture is wrong.
    Final Answer:
    Hence, the counterexample for the given example i.e. “If A, B and C are collinear, then AB + BC = AC” is the above diagram.
    General
    Maths-

    After an oil pipeline burst one morning, gas prices went up by $2.20 per gallon. If that afternoon you bought 10 gallons of gas for $53.90, what was the price per gallon before the oil pipeline burst that morning?

    • Hint:
    ○ Form the eqaution using given information.
    ○ Take variable value as any alphabet.
    ○ Take terms with cofficient at one side and without cofficients at another side.
    • Step-by-step explanation:
    ○ Given:
    Increase price per gallon = $2.20.
    No of gallons of gas brought = 10.
    Total money paid = $53.90.
    ○ Step 1:
    Let the original price of one gallon of gas be x.
    So,
    Price of 1 gallon of gas after burst = original price + increase in price
    Price of 1 gallon of gas after burst = x + 2.20
    ○ Step 2:
    ○ Total selling price.
    Price of 1 gallon of gas after burst = x + 2.20
    Price of 10 gallon of gas after burst = (x + 2.20) cross times 10
    rightwards double arrow10x + 22
    As it is given total money paid is $53.90
    ∴ 10x + 22 = 53.90
    rightwards double arrow10x = 53.90 - 22
    rightwards double arrow10x = 31.90
    rightwards double arrowx = fraction numerator 31.90 over denominator 10 end fraction
    rightwards double arrowx = 3.190
    • Final Answer:
    Hence, the original price of one gallon of gas is $3.190.

    After an oil pipeline burst one morning, gas prices went up by $2.20 per gallon. If that afternoon you bought 10 gallons of gas for $53.90, what was the price per gallon before the oil pipeline burst that morning?

    Maths-General
    • Hint:
    ○ Form the eqaution using given information.
    ○ Take variable value as any alphabet.
    ○ Take terms with cofficient at one side and without cofficients at another side.
    • Step-by-step explanation:
    ○ Given:
    Increase price per gallon = $2.20.
    No of gallons of gas brought = 10.
    Total money paid = $53.90.
    ○ Step 1:
    Let the original price of one gallon of gas be x.
    So,
    Price of 1 gallon of gas after burst = original price + increase in price
    Price of 1 gallon of gas after burst = x + 2.20
    ○ Step 2:
    ○ Total selling price.
    Price of 1 gallon of gas after burst = x + 2.20
    Price of 10 gallon of gas after burst = (x + 2.20) cross times 10
    rightwards double arrow10x + 22
    As it is given total money paid is $53.90
    ∴ 10x + 22 = 53.90
    rightwards double arrow10x = 53.90 - 22
    rightwards double arrow10x = 31.90
    rightwards double arrowx = fraction numerator 31.90 over denominator 10 end fraction
    rightwards double arrowx = 3.190
    • Final Answer:
    Hence, the original price of one gallon of gas is $3.190.
    parallel
    General
    Maths-

    Show the conjecture is false by finding a counterexample. Two supplementary angles form a linear pair.

    Hint:
    Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.
    Counterexample: It is an example which shows that the conjecture is false.
    Solution
    If we take a parallelogram

    Here, we know that angles a and b are supplementary angles. But they are not linear.
    So, the given conjecture is wrong.
    Final Answer:
    Hence, the counterexample of the given conjecture i.e. “Two supplementary angles form a linear pair.” is the adjacent angles of a parallelogram.

    Show the conjecture is false by finding a counterexample. Two supplementary angles form a linear pair.

    Maths-General
    Hint:
    Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.
    Counterexample: It is an example which shows that the conjecture is false.
    Solution
    If we take a parallelogram

    Here, we know that angles a and b are supplementary angles. But they are not linear.
    So, the given conjecture is wrong.
    Final Answer:
    Hence, the counterexample of the given conjecture i.e. “Two supplementary angles form a linear pair.” is the adjacent angles of a parallelogram.
    General
    Maths-

    A store had homemade sweaters on sale for $20 off the original price. Aunt Ethel jumped at the bargain and bought a sweater for all 15 members of her family. If Aunt Ethel paid $375 for all the sweaters, what was the original price of each sweater?

    • Hint:
    ○ Form the eqaution using given information.
    ○ Take variable value as any alphabet.
    ○ Take terms with cofficient at one side and without cofficients at another side.
    • Step-by-step explanation:
    ○ Given:
    Discount per sweater = $20.
    No of sweaters brought = 15.
    Total money paid = $375.
    ○ Step 1:
    Let the original price of one sweater be x.
    So,
    Selling price of 1 sweater  = original price - discount
    Selling price of 1 sweater  = x - 20
    ○ Step 2:
    ○ Total selling price.
    As 1 sweater cost (x-20)
    So, 15 sweater will cost
    rightwards double arrow15(x - 20) = 15x - 300
    As it is given total money paid is $375
    ∴ 15x - 300 = 375
    rightwards double arrow15x = 375 + 300
    rightwards double arrow15x = 675
    rightwards double arrowx = 675 over 15
    rightwards double arrowx = 45
    • Final Answer:
    Hence, the original price of sweater is $45.

    A store had homemade sweaters on sale for $20 off the original price. Aunt Ethel jumped at the bargain and bought a sweater for all 15 members of her family. If Aunt Ethel paid $375 for all the sweaters, what was the original price of each sweater?

    Maths-General
    • Hint:
    ○ Form the eqaution using given information.
    ○ Take variable value as any alphabet.
    ○ Take terms with cofficient at one side and without cofficients at another side.
    • Step-by-step explanation:
    ○ Given:
    Discount per sweater = $20.
    No of sweaters brought = 15.
    Total money paid = $375.
    ○ Step 1:
    Let the original price of one sweater be x.
    So,
    Selling price of 1 sweater  = original price - discount
    Selling price of 1 sweater  = x - 20
    ○ Step 2:
    ○ Total selling price.
    As 1 sweater cost (x-20)
    So, 15 sweater will cost
    rightwards double arrow15(x - 20) = 15x - 300
    As it is given total money paid is $375
    ∴ 15x - 300 = 375
    rightwards double arrow15x = 375 + 300
    rightwards double arrow15x = 675
    rightwards double arrowx = 675 over 15
    rightwards double arrowx = 45
    • Final Answer:
    Hence, the original price of sweater is $45.
    General
    Maths-

    Gym charges a $50 activation fee and $17 per month for a membership. If you spend $356, for how many months do you have a gym membership?

    • Hint:
    ○ Form the eqaution using given information.
    ○ Solve the equation.
    ○ Take terms with cofficient at one side and without cofficient at another side.
    • Step by step explanation:
    ○ Given:
    Activation fee for gym = $50.
    Membership per month = $17.
    Total money spent = $356.
    ○ Step 1:
    Let you had membership for x months.
    So,
    Total amount paid for 1 month  = activation fee + monthly membership
    Total amount paid for 1 month  =  50 + 17
    Hence,
    Total amount paid for x month  = activation fee + membership for x month
    Total amount paid for x month  =  50 + 17x
    ○ Step 2:
    ○ As total amount paid is $356.
    ∴ 50 + 17x = 356
    rightwards double arrow17x =  356 - 50
    rightwards double arrow17x = 306
    rightwards double arrowx = 306 over 17
    rightwards double arrowx = 18
    • Final Answer:
    Hence, for 18 months you had membership.

    Gym charges a $50 activation fee and $17 per month for a membership. If you spend $356, for how many months do you have a gym membership?

    Maths-General
    • Hint:
    ○ Form the eqaution using given information.
    ○ Solve the equation.
    ○ Take terms with cofficient at one side and without cofficient at another side.
    • Step by step explanation:
    ○ Given:
    Activation fee for gym = $50.
    Membership per month = $17.
    Total money spent = $356.
    ○ Step 1:
    Let you had membership for x months.
    So,
    Total amount paid for 1 month  = activation fee + monthly membership
    Total amount paid for 1 month  =  50 + 17
    Hence,
    Total amount paid for x month  = activation fee + membership for x month
    Total amount paid for x month  =  50 + 17x
    ○ Step 2:
    ○ As total amount paid is $356.
    ∴ 50 + 17x = 356
    rightwards double arrow17x =  356 - 50
    rightwards double arrow17x = 306
    rightwards double arrowx = 306 over 17
    rightwards double arrowx = 18
    • Final Answer:
    Hence, for 18 months you had membership.
    parallel
    General
    Maths-

    State the law of logic that is illustrated.
    If you score more than 75%, then you can go to the beach.
    If you go to the beach, then you can surf.
    If you score more than 75%. Then you can surf

    Hint:
    Law of Syllogism states that:
    1) if p  q is true
    2) If q  r is true
    then we can conclude that p not stretchy rightwards arrow r is also true.
    Solution
    It is given that: If you score more than 75%, then you can go to the beach, If you go to the beach, then you can surf and If you score more than 75%. Then you can surf. So if we take
    p = Score is more than 75%
    q = You can go to the beach
    r = You can surf
    So can write the given statement “If you score more than 75%, then you can go to the beach” as
    pnot stretchy rightwards arrow  q and the statement “If you go to the beach, then you can surf” can be written as q  not stretchy rightwards arrow r and also the statement “If you score more than 75%. Then you can surf” can be written as pnot stretchy rightwards arrow r.
    So we can see that we are given: pnot stretchy rightwards arrow q is true
    not stretchy rightwards arrow  r is true
    not stretchy rightwards arrow  r is true
    This statement resolves the law of syllogism which states that if p not stretchy rightwards arrow q is true and If qnot stretchy rightwards arrow  r is true then we can conclude that p not stretchy rightwards arrow  r is also true
    Final Answer:
    Hence, the law of logic which is used in these statements is the law of syllogism.

    State the law of logic that is illustrated.
    If you score more than 75%, then you can go to the beach.
    If you go to the beach, then you can surf.
    If you score more than 75%. Then you can surf

    Maths-General
    Hint:
    Law of Syllogism states that:
    1) if p  q is true
    2) If q  r is true
    then we can conclude that p not stretchy rightwards arrow r is also true.
    Solution
    It is given that: If you score more than 75%, then you can go to the beach, If you go to the beach, then you can surf and If you score more than 75%. Then you can surf. So if we take
    p = Score is more than 75%
    q = You can go to the beach
    r = You can surf
    So can write the given statement “If you score more than 75%, then you can go to the beach” as
    pnot stretchy rightwards arrow  q and the statement “If you go to the beach, then you can surf” can be written as q  not stretchy rightwards arrow r and also the statement “If you score more than 75%. Then you can surf” can be written as pnot stretchy rightwards arrow r.
    So we can see that we are given: pnot stretchy rightwards arrow q is true
    not stretchy rightwards arrow  r is true
    not stretchy rightwards arrow  r is true
    This statement resolves the law of syllogism which states that if p not stretchy rightwards arrow q is true and If qnot stretchy rightwards arrow  r is true then we can conclude that p not stretchy rightwards arrow  r is also true
    Final Answer:
    Hence, the law of logic which is used in these statements is the law of syllogism.
    General
    Maths-

    Show the conjecture is false by finding a counterexample. Two adjacent angles always form a linear pair.

    Hint:
    Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.
    Counterexample: It is an example which shows that the conjecture is false.
    Solution
    Linear pairs are always supplementary but adjacent angles may not be. It can be shown by the following
    diagram:

    Here, we can see that the sum of adjacent angles will be definitely less than 180o. So, the given conjecture is wrong.
    Final Answer:
    Hence, the counterexample for the given conjecture is the above figure.

    Show the conjecture is false by finding a counterexample. Two adjacent angles always form a linear pair.

    Maths-General
    Hint:
    Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.
    Counterexample: It is an example which shows that the conjecture is false.
    Solution
    Linear pairs are always supplementary but adjacent angles may not be. It can be shown by the following
    diagram:

    Here, we can see that the sum of adjacent angles will be definitely less than 180o. So, the given conjecture is wrong.
    Final Answer:
    Hence, the counterexample for the given conjecture is the above figure.
    General
    Maths-

    Prove that ∠ ABC ≅ ∠ ADC

    Complete step by step solution:
    From the figure,
    In △ABC and △CDA, we have
    AB = CD (given)
    AD = CB (given)
    AC = AC (common side)
    Hence △ABC⩭ △CDA by SSS congruence rule.
    ⇒ ∠ ABC ≅ ∠ CDA (corresponding parts of congruent triangles)

    Prove that ∠ ABC ≅ ∠ ADC

    Maths-General
    Complete step by step solution:
    From the figure,
    In △ABC and △CDA, we have
    AB = CD (given)
    AD = CB (given)
    AC = AC (common side)
    Hence △ABC⩭ △CDA by SSS congruence rule.
    ⇒ ∠ ABC ≅ ∠ CDA (corresponding parts of congruent triangles)
    parallel
    General
    Maths-

    A man bought 4 cups of coffee and left a $7 tip. A woman bought 8 cups of coffee and only left a $2 tip. If they paid the same amount, how much was each cup of coffee?

    • Hint:
    ○ Solve the equation.
    ○ Take terms with cofficient at one side and without cofficient at another side.
    • Step by step explanation:
    ○ Given:
    A man bought 4 cups of coffee and left a $7 tip.
    A woman bought 8 cups of coffee and only left a $2 tip.
    Amount paid by both is same.
    ○ Step 1:
    Let the price of 1 cup of coffee be x.
    So, in case of man,
    Total amount paid  = 4x + 7   { %7 is tip }
    In case of women,
    Total amount paid  = 8x + 2   { %2 is tip }
    ○ Step 2:
    ○ As amount paid by both of them is same.
    ∴ 4x + 7 = 8x + 2
    rightwards double arrow7 - 2 = 8x - 4x
    rightwards double arrow5 = 4x
    rightwards double arrowx = 5 over 4
    rightwards double arrowx = 1.25
    • Final Answer:
    Hence, each cup of coffee cost $1.25.

    A man bought 4 cups of coffee and left a $7 tip. A woman bought 8 cups of coffee and only left a $2 tip. If they paid the same amount, how much was each cup of coffee?

    Maths-General
    • Hint:
    ○ Solve the equation.
    ○ Take terms with cofficient at one side and without cofficient at another side.
    • Step by step explanation:
    ○ Given:
    A man bought 4 cups of coffee and left a $7 tip.
    A woman bought 8 cups of coffee and only left a $2 tip.
    Amount paid by both is same.
    ○ Step 1:
    Let the price of 1 cup of coffee be x.
    So, in case of man,
    Total amount paid  = 4x + 7   { %7 is tip }
    In case of women,
    Total amount paid  = 8x + 2   { %2 is tip }
    ○ Step 2:
    ○ As amount paid by both of them is same.
    ∴ 4x + 7 = 8x + 2
    rightwards double arrow7 - 2 = 8x - 4x
    rightwards double arrow5 = 4x
    rightwards double arrowx = 5 over 4
    rightwards double arrowx = 1.25
    • Final Answer:
    Hence, each cup of coffee cost $1.25.
    General
    Maths-

    Prove that ∠ ABC ≅  ∠ PQR

    Complete step by step solution:
    Consider 2 triangles, and
    From the figure, we have
    ∠ BAC = ∠ QPR (given)
    ∠ BCA = ∠ QRP (given)
    By angle sum property
    We have, ∠ ABC = ∠ PQR
    Ie, ∠ ABC = 180°- (∠ BAC + ∠ BCA) and
    ∠ PQR = 180°- (∠ QPR + ∠ QRP) = 180° - (∠ BAC + ∠ BCA)
    So, ⇒ ∠ ABC ≅ ∠ PQR

    Prove that ∠ ABC ≅  ∠ PQR

    Maths-General
    Complete step by step solution:
    Consider 2 triangles, and
    From the figure, we have
    ∠ BAC = ∠ QPR (given)
    ∠ BCA = ∠ QRP (given)
    By angle sum property
    We have, ∠ ABC = ∠ PQR
    Ie, ∠ ABC = 180°- (∠ BAC + ∠ BCA) and
    ∠ PQR = 180°- (∠ QPR + ∠ QRP) = 180° - (∠ BAC + ∠ BCA)
    So, ⇒ ∠ ABC ≅ ∠ PQR
    General
    Maths-

    Show the conjecture is false by finding a counterexample. If stack A B with _ below ≅ stack B C with _ below, then point B is the midpoint of AB.

    Hint:
    Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.
    Counterexample: It is an example which shows that the conjecture is false.
    Solution
                  
    In the above diagram we can see that AB = BC, but point B is not on AC.
    So the conjunction is false
    Final Answer:
    Hence, the diagram is the counterexample of the given conjecture.

    Show the conjecture is false by finding a counterexample. If stack A B with _ below ≅ stack B C with _ below, then point B is the midpoint of AB.

    Maths-General
    Hint:
    Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.
    Counterexample: It is an example which shows that the conjecture is false.
    Solution
                  
    In the above diagram we can see that AB = BC, but point B is not on AC.
    So the conjunction is false
    Final Answer:
    Hence, the diagram is the counterexample of the given conjecture.
    parallel
    General
    Maths-

    A store discounted the price of Doritos $0.35 and then a man bought 5 bags. If he paid a total of $12.70 for the bags of chips, how much was each bag originally?

    ○ Given:
    Discount on 1 pack of Doritos = $.0.35.
    Total pack brought = 5.
    Total money paid = $12.70.
    ○ Step 1:
    ○ Total discount;
    Discount on 1 pack of Doritos= $.0.35
    So,
    Discount on 5 pack of Doritos= $.0.35 cross times 5 = $ 1.75
    ○ Step 2:
    ○ Original price of 5 bags Doritos:
    It is given that price of 5 bags  after discount is $12.70
    So, original price of 5 bags = 12.70 + 1.75 = 14.45
    ○ Step 3:
    ○ Original price of 1 bag:
    original price of 5 bags = $ 14.45
    original price of 1 bags = $ fraction numerator 14.45 over denominator 5 end fraction = 2.89
    • Final Answer:
    Hence, the original price of one bag of Doritos is $2.89.

    A store discounted the price of Doritos $0.35 and then a man bought 5 bags. If he paid a total of $12.70 for the bags of chips, how much was each bag originally?

    Maths-General
    ○ Given:
    Discount on 1 pack of Doritos = $.0.35.
    Total pack brought = 5.
    Total money paid = $12.70.
    ○ Step 1:
    ○ Total discount;
    Discount on 1 pack of Doritos= $.0.35
    So,
    Discount on 5 pack of Doritos= $.0.35 cross times 5 = $ 1.75
    ○ Step 2:
    ○ Original price of 5 bags Doritos:
    It is given that price of 5 bags  after discount is $12.70
    So, original price of 5 bags = 12.70 + 1.75 = 14.45
    ○ Step 3:
    ○ Original price of 1 bag:
    original price of 5 bags = $ 14.45
    original price of 1 bags = $ fraction numerator 14.45 over denominator 5 end fraction = 2.89
    • Final Answer:
    Hence, the original price of one bag of Doritos is $2.89.
    General
    Maths-

    Use the Law of Detachment to make a valid conclusion in the true situation.
    If the measure of an angle is less than 90°, then it is an acute angle.
    m straight angle Q equals 165 to the power of ring operator

    Hint:
    Law of Detachment states that if p not stretchy rightwards arrow q is true and it is given that p is true then we can conclude 
    that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.
    Solution
    Consider the statement into two separate statements
    p: The measure of an angle is less than 90°
    q: The angle is an acute angle.
    So we can write the given statement “If the measure of an angle is less than 90°, then it is an acute angle” as:
    p not stretchy rightwards arrow q
    It is given that
    𝑚∠𝑄 = 165°
    Angle Q is greater than 90o which means the p statement is false and hence we cannot conclude anything.
    Final Answer:
    Hence, we are unable to conclude anything.

    Use the Law of Detachment to make a valid conclusion in the true situation.
    If the measure of an angle is less than 90°, then it is an acute angle.
    m straight angle Q equals 165 to the power of ring operator

    Maths-General
    Hint:
    Law of Detachment states that if p not stretchy rightwards arrow q is true and it is given that p is true then we can conclude 
    that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.
    Solution
    Consider the statement into two separate statements
    p: The measure of an angle is less than 90°
    q: The angle is an acute angle.
    So we can write the given statement “If the measure of an angle is less than 90°, then it is an acute angle” as:
    p not stretchy rightwards arrow q
    It is given that
    𝑚∠𝑄 = 165°
    Angle Q is greater than 90o which means the p statement is false and hence we cannot conclude anything.
    Final Answer:
    Hence, we are unable to conclude anything.
    General
    Maths-

    Find JK

    Complete step by step solution:
    Consider 2 triangles, and
    From the figure, we have
    JL = OQ = 5 (given)
    ∠ JLK = ∠ OQP (given)
    KL = PQ = 7 (given)
    ∴ △ KJL ⩭ △ POQ by SAS congruence rule.
    ⇒ JK = OP (corresponding parts of congruent triangles)
    ⇒ JK = 8

    Find JK

    Maths-General
    Complete step by step solution:
    Consider 2 triangles, and
    From the figure, we have
    JL = OQ = 5 (given)
    ∠ JLK = ∠ OQP (given)
    KL = PQ = 7 (given)
    ∴ △ KJL ⩭ △ POQ by SAS congruence rule.
    ⇒ JK = OP (corresponding parts of congruent triangles)
    ⇒ JK = 8
    parallel

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