Maths-
General
Easy
Question
Hint:
Hint :-Using the ratio, find the individual angels in terms of k .Now using sum of angles of triangle is 180° find the value of k and actual value of angles
Ans :- 50°,60° and 70°
The correct answer is: Therefore 50°,60° and 70° are the angles of the triangle which satisfy the condition.
Explanation :-
Given angles are in the ratio 5:6:7
Step 1:- Find angles in terms of k and find k
The angles are 5k ,6k and 7 k respectively
We know Sum of angles of triangle is 180°
5k +6k+7k = 180
18 k = 180
K = 10°
Step 2:- Find the actual angles of triangle
5k = 5×10 = 50°
6k = 6×10 = 60°
7k = 7×10 = 70°
Therefore 50°,60° and 70° are the angles of the triangle which satisfy the condition .
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Maths-
Maths-General
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The Quadrilateral PQRS has angles at S,Q right angles and the diagonals PR, QS are perpendicular. Prove that SR = QR.
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)
The Quadrilateral PQRS has angles at S,Q right angles and the diagonals PR, QS are perpendicular. Prove that SR = QR.
![](data:image/png;base64,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)
Maths-General
Maths-
P and Q are points on the sides CA and CB respectively of a
right angled at c. Prove that ![AQ squared plus BP squared equals](data:image/png;base64,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)
![A B squared plus P Q squared](data:image/png;base64,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)
P and Q are points on the sides CA and CB respectively of a
right angled at c. Prove that ![AQ squared plus BP squared equals](data:image/png;base64,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)
![A B squared plus P Q squared](data:image/png;base64,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)
Maths-General
Maths-
In △ABC, ∠B=90∘ and is the mid point of BC. Prove that ![A C squared minus A D squared equals 3 B D squared](data:image/png;base64,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)
In △ABC, ∠B=90∘ and is the mid point of BC. Prove that ![A C squared minus A D squared equals 3 B D squared](data:image/png;base64,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)
Maths-General
Maths-
Maths-General
Maths-
The perpendicular AD on the base BC of Triangle ABC intersects BC in D such that BD = 3CD. Prove that
![2 A B squared equals 2 A C squared plus B C squared](data:image/png;base64,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)
The perpendicular AD on the base BC of Triangle ABC intersects BC in D such that BD = 3CD. Prove that
![2 A B squared equals 2 A C squared plus B C squared](data:image/png;base64,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)
Maths-General
Maths-
In an equilateral
the side BC is trisected at D . Prove that ![9 A D squared equals 7 A B squared](data:image/png;base64,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)
.
In an equilateral
the side BC is trisected at D . Prove that ![9 A D squared equals 7 A B squared](data:image/png;base64,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)
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Maths-General
Maths-
![](data:image/png;base64,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)
ABC and DBC are two isosceles triangles on the same base BC. Show
that ![straight angle ABD equals straight angle ACD](data:image/png;base64,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)
![](data:image/png;base64,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)
ABC and DBC are two isosceles triangles on the same base BC. Show
that ![straight angle ABD equals straight angle ACD](data:image/png;base64,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)
Maths-General
Maths-
PQ and RS are respectively the smallest and longest sides of a quadrilateral PQRS. Show that ∠ P > ∠ R
PQ and RS are respectively the smallest and longest sides of a quadrilateral PQRS. Show that ∠ P > ∠ R
Maths-General
Maths-
Classify whether the following Surd is rational or irrational , justify. 3√24− 5√5
Classify whether the following Surd is rational or irrational , justify. 3√24− 5√5
Maths-General
Maths-
In △ABC, AD and are the bisectors of ∠A and ∠C respectively. AD and CE intersect at . If ∠ABC = 90^∘, then find ∠AOC.
In △ABC, AD and are the bisectors of ∠A and ∠C respectively. AD and CE intersect at . If ∠ABC = 90^∘, then find ∠AOC.
Maths-General
Maths-
Maths-General
Maths-
Classify whether the following Surd is rational or irrational , justify 4√5+ 9
Classify whether the following Surd is rational or irrational , justify 4√5+ 9
Maths-General
Maths-
PQR is a triangle in which PQ=PR.S is any point on the side PQ. Through S, a line is drawn parallel to QR intersecting PR at T. Prove that PS = PT.
PQR is a triangle in which PQ=PR.S is any point on the side PQ. Through S, a line is drawn parallel to QR intersecting PR at T. Prove that PS = PT.
Maths-General
Maths-
Maths-General