Question
Find the length of each side of the given regular dodecagon.

The correct answer is: - 16
Solution:
Hint:
- A regular dodecagon has 12 sides equal in length and all the angles have equal measures, all the 12 vertices are equidistant from the center of dodecagon.
- A regular dodecagon is a symmetrical polygon.
Explanation:
- We have been given in the question figure of a regular dodecagon
- We have also been given the two sides of it that is -
- We have to find length of each side of the regular dodecagon.
We have given a regular dodecagon with sides represented as 
Since, It is regular, then all sides are equal
So,

2x - 1 = 9x + 15
7x = - 16
X can not be negative
Wrong data
Related Questions to study
Draw a quadrilateral that is not regular.
Hint:
- A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices, and four angles.
- We have been given information in the question to draw a quadrilateral that is not regular.
Draw a quadrilateral that is not regular.
Hint:
- A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices, and four angles.
- We have been given information in the question to draw a quadrilateral that is not regular.
Which of the statements is TRUE?
- We have been given four statements in the question from which we have to choose which statement is true.
- In the given four statements we have been given information about the semicircle, concave polygon, triangle and regular polygon.
Option A:
A semicircle is a polygon.
No this is not true, because polygon only contain straight lines.
Option B:
A concave polygon is regular
It is not necessary that a concave polygon is regular.
So, it is not true
Option C:
A regular polygon is equiangular
Yes this is true, a regular polygon is equiangular and equilateral.
Option D:
Every triangle is regular
This is not true, because mant triangles are not regulat.
Hence, Option C is correct.
Which of the statements is TRUE?
- We have been given four statements in the question from which we have to choose which statement is true.
- In the given four statements we have been given information about the semicircle, concave polygon, triangle and regular polygon.
Option A:
A semicircle is a polygon.
No this is not true, because polygon only contain straight lines.
Option B:
A concave polygon is regular
It is not necessary that a concave polygon is regular.
So, it is not true
Option C:
A regular polygon is equiangular
Yes this is true, a regular polygon is equiangular and equilateral.
Option D:
Every triangle is regular
This is not true, because mant triangles are not regulat.
Hence, Option C is correct.
The length of each side of a nonagon is 8 in. Find its perimeter
Hint:
- A nonagon is a polygon with nine sides and nine angles which can be regular, irregular, concave or convex depending upon its sides and interior angles.
- We have been given the length of each side of a nonagon that is 8 in.
- We have to find the perimeter of the given nonagon.
We have length of each side of a nanagon 8in
Now the perimeter will be
9 × 8in
72in
Hence, Option C is correct.
The length of each side of a nonagon is 8 in. Find its perimeter
Hint:
- A nonagon is a polygon with nine sides and nine angles which can be regular, irregular, concave or convex depending upon its sides and interior angles.
- We have been given the length of each side of a nonagon that is 8 in.
- We have to find the perimeter of the given nonagon.
We have length of each side of a nanagon 8in
Now the perimeter will be
9 × 8in
72in
Hence, Option C is correct.
The lengths (in inches) of two sides of a regular pentagon are represented by the expressions 4x + 7 and x + 16. Find the length of a side of the pentagon.
Hint:
- A regular pentagon is a polygon that has 5 sides all of same length and all the angles of the same measure.
- We have been given the two sides of a regular pentagon in the form of expressions that is -
- 4x + 7 and x + 16
- We have to find the length of a side of the pentagon.
The length of the two sides of a regular pentagon is represented by x + 16; 4x + 7
Now, We know that all sides of regular polygon are equal.
So,
X + 16 = 4x + 7
3x = 16 - 7
3x = 9
x = 3
And the measure of length will be
= x + 16
= 3 + 16
= 19
The lengths (in inches) of two sides of a regular pentagon are represented by the expressions 4x + 7 and x + 16. Find the length of a side of the pentagon.
Hint:
- A regular pentagon is a polygon that has 5 sides all of same length and all the angles of the same measure.
- We have been given the two sides of a regular pentagon in the form of expressions that is -
- 4x + 7 and x + 16
- We have to find the length of a side of the pentagon.
The length of the two sides of a regular pentagon is represented by x + 16; 4x + 7
Now, We know that all sides of regular polygon are equal.
So,
X + 16 = 4x + 7
3x = 16 - 7
3x = 9
x = 3
And the measure of length will be
= x + 16
= 3 + 16
= 19
Two angles of a regular polygon are given to be
Find the value of and measure of each angle.
Hint:
- A polygon whose length of all sides is equal with equal angles at each vertex is called regular polygon.
- We have been given the two sides of a regular polygon that is - (2𝑥 + 27)° 𝑎𝑛𝑑 (3𝑥 − 3)°
- We have to find the value of x and measure of each angle.
We know that a regulat polygon is equiangular
So,
2x + 27 = 3x - 3
x = 27 + 3
x = 30
And the value of each angle will be
= 2x + 27
= 2(30) + 27
= 87
Two angles of a regular polygon are given to be
Find the value of and measure of each angle.
Hint:
- A polygon whose length of all sides is equal with equal angles at each vertex is called regular polygon.
- We have been given the two sides of a regular polygon that is - (2𝑥 + 27)° 𝑎𝑛𝑑 (3𝑥 − 3)°
- We have to find the value of x and measure of each angle.
We know that a regulat polygon is equiangular
So,
2x + 27 = 3x - 3
x = 27 + 3
x = 30
And the value of each angle will be
= 2x + 27
= 2(30) + 27
= 87
Solve the equation. Write a reason for each step.
8(−x − 6) = −50 − 10x
Ans:- x = 1
Explanation :-
Given ,8(-x − 6) = -50-10x.
By left distributive property - 8x − 48 = - 50 -10x
Adding 48 on both sides by additive property of equality both sides remain equal.
- 8x − 48 + 48 = - 50 -10x + 48
- 8x = -10x - 2
Adding 10x on both sides by additive property of equality both sides remain equal.
- 8x +10x = -10x - 2 +10x
2x = - 2
Dividing 2
x = -1
∴ x = -1
Solve the equation. Write a reason for each step.
8(−x − 6) = −50 − 10x
Ans:- x = 1
Explanation :-
Given ,8(-x − 6) = -50-10x.
By left distributive property - 8x − 48 = - 50 -10x
Adding 48 on both sides by additive property of equality both sides remain equal.
- 8x − 48 + 48 = - 50 -10x + 48
- 8x = -10x - 2
Adding 10x on both sides by additive property of equality both sides remain equal.
- 8x +10x = -10x - 2 +10x
2x = - 2
Dividing 2
x = -1
∴ x = -1
Find the measure of each angle of an equilateral triangle using base angle theorem.
Hint:
- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- An equilateral triangle is a triangle with all the three sides of equal length.
- We have to find the measure of each angle of an equilateral triangle using base angle theorem.
Let a triangle be ABC
Here,
AB = AC
Using base angle theorem
And,
So,
Therefore,
Step 2 of 2:
We know that the sum of all angles of a triangle is 1800.
Now,
So,
Find the measure of each angle of an equilateral triangle using base angle theorem.
Hint:
- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- An equilateral triangle is a triangle with all the three sides of equal length.
- We have to find the measure of each angle of an equilateral triangle using base angle theorem.
Let a triangle be ABC
Here,
AB = AC
Using base angle theorem
And,
So,
Therefore,
Step 2 of 2:
We know that the sum of all angles of a triangle is 1800.
Now,
So,
The length of each side of a regular pentagon is . Find the value of if its perimeter is .
Hint:
- A regular pentagon is a polygon that has 5 sides all of same length and all the angles of the same measure.
- We have been given in the question the length of each side of a regular pentagon which is (x+5) cm
- We have also been given the perimeter that is 50 cm.
- We have to find the value of x.
We have given a perimeter of a regular pentaogn 50.
A pentagon has sides.
The length of the side is x+5
So,
5(x + 5) = 50
x + 5 = 10
x = 5
Hence, Option A is correct.
The length of each side of a regular pentagon is . Find the value of if its perimeter is .
Hint:
- A regular pentagon is a polygon that has 5 sides all of same length and all the angles of the same measure.
- We have been given in the question the length of each side of a regular pentagon which is (x+5) cm
- We have also been given the perimeter that is 50 cm.
- We have to find the value of x.
We have given a perimeter of a regular pentaogn 50.
A pentagon has sides.
The length of the side is x+5
So,
5(x + 5) = 50
x + 5 = 10
x = 5
Hence, Option A is correct.
Name the property of equality the statement illustrates.
Every segment is congruent to itself.
Ans :- Option A
Explanation :-
The reflexive property states that any real number, a, is equal to itself. That is, a = a.
Similarly the segment is congruent to itself .
∴Option A
Name the property of equality the statement illustrates.
Every segment is congruent to itself.
Ans :- Option A
Explanation :-
The reflexive property states that any real number, a, is equal to itself. That is, a = a.
Similarly the segment is congruent to itself .
∴Option A
Hint:
- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- We have been given a diagram of a triangle in the question named ABC we have also been given 𝑚∠𝐵 = 55°.
- We have to find out 𝑚∠A.
We have given figure
Here, AB = AC
It means the given triangle is an isosceles triangle.
Now,
By base angle theorem
And it is given
So,
Step 2 of 2:
We know that the sum of angle of a triangle is 1800
Hint:
- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- We have been given a diagram of a triangle in the question named ABC we have also been given 𝑚∠𝐵 = 55°.
- We have to find out 𝑚∠A.
We have given figure
Here, AB = AC
It means the given triangle is an isosceles triangle.
Now,
By base angle theorem
And it is given
So,
Step 2 of 2:
We know that the sum of angle of a triangle is 1800
If f(x) satisfies the relation 2f(x) +f(1-x) = x2 for all real x , then f(x) is
We have given that
2f(x) +f(1-x) = x2 - - -- - - - - -(i)
We have to find the value of f(x)
By replacing x by (1-x) in equation (i)we get,
2f(1-x) + f(x) = (1-x)2
2f(1-x) + f(x) = 1 + x2 – 2x - - - - - -(ii)
Multiplying the equation(i) by 2 we get,
4f(x) + 2f(1-x) = 2x2 - - - - - - (iii)
Subtracting equation (ii) from (iii)
3f(x) = x2 + 2x -1
So,
Therefore option (b) is correct.
If f(x) satisfies the relation 2f(x) +f(1-x) = x2 for all real x , then f(x) is
We have given that
2f(x) +f(1-x) = x2 - - -- - - - - -(i)
We have to find the value of f(x)
By replacing x by (1-x) in equation (i)we get,
2f(1-x) + f(x) = (1-x)2
2f(1-x) + f(x) = 1 + x2 – 2x - - - - - -(ii)
Multiplying the equation(i) by 2 we get,
4f(x) + 2f(1-x) = 2x2 - - - - - - (iii)
Subtracting equation (ii) from (iii)
3f(x) = x2 + 2x -1
So,
Therefore option (b) is correct.
If f:R->R be a function whose inverse is (𝑥+5)/3 , then what is the value of f(x)
f-1(x) = (x+5)/3
For solving this let us take
y = f-1(x)
y = (x+5)/3
Further solving we get,
x = 3y – 5
f(y) = 3y – 5
Therefore,
f(x) = 3x – 5
If f:R->R be a function whose inverse is (𝑥+5)/3 , then what is the value of f(x)
f-1(x) = (x+5)/3
For solving this let us take
y = f-1(x)
y = (x+5)/3
Further solving we get,
x = 3y – 5
f(y) = 3y – 5
Therefore,
f(x) = 3x – 5
Hint:
- The base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- We have been given in the question a diagram of a triangle named ABC and 𝑚∠𝐴 = 60°.
- We have to find the 𝑚∠𝐴 𝑎𝑛𝑑 𝑚∠𝐶.
In the given figure, AB = AC.
So, ABC is an isosceles triangle.
So, According to base-angle theorem, the angles opposite the congruent sides are congruent.
So,
Step 2 of 2:
Now we know that the sum of angle of triangle is equal to 1800.
So,
Since,
So,
Therefore,
Hint:
- The base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- We have been given in the question a diagram of a triangle named ABC and 𝑚∠𝐴 = 60°.
- We have to find the 𝑚∠𝐴 𝑎𝑛𝑑 𝑚∠𝐶.
In the given figure, AB = AC.
So, ABC is an isosceles triangle.
So, According to base-angle theorem, the angles opposite the congruent sides are congruent.
So,
Step 2 of 2:
Now we know that the sum of angle of triangle is equal to 1800.
So,
Since,
So,
Therefore,
Let A= {x, y, z} and B= { p, q, r, s}, What is the number of distinct relations from B to A ?
A= {x, y, z}
B= { p, q, r, s},
For finding the district relations from B to A we have to take the cartesian product of B and A
B×A = {p, q, r, s} × {x, y, z}
= {(p, x) , (p, y) , (p, z) , (q, x) , (q, y), (q, z) , (r, x) , (r, y), (r, z) , (s, x), (s, y), (s, z)}
Therefore there are 12 distinct relations .
Let A= {x, y, z} and B= { p, q, r, s}, What is the number of distinct relations from B to A ?
A= {x, y, z}
B= { p, q, r, s},
For finding the district relations from B to A we have to take the cartesian product of B and A
B×A = {p, q, r, s} × {x, y, z}
= {(p, x) , (p, y) , (p, z) , (q, x) , (q, y), (q, z) , (r, x) , (r, y), (r, z) , (s, x), (s, y), (s, z)}
Therefore there are 12 distinct relations .
Let f, g : R→R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and f(g)
f(x) = x + 1
g(x) = 2x – 3
We have to find the value of
i) f(x) + g(x)
ii) f(x) – g(x)
iii) f(g(x))
Therefore,
i) f(x) + g(x) = x + 1 + 2x – 3
= 3x – 2
ii f(x) – g(x) = x + 1 – (2x – 3)
= x + 1 – 2x + 3
= 4 – x
iii) f(g(x)) = f(2x -3)
= (2x – 3) + 1
= 2x – 2
Therefore, f+g = 3x – 2
f – g = 4 – x
f(g) = 2x – 2
Let f, g : R→R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and f(g)
f(x) = x + 1
g(x) = 2x – 3
We have to find the value of
i) f(x) + g(x)
ii) f(x) – g(x)
iii) f(g(x))
Therefore,
i) f(x) + g(x) = x + 1 + 2x – 3
= 3x – 2
ii f(x) – g(x) = x + 1 – (2x – 3)
= x + 1 – 2x + 3
= 4 – x
iii) f(g(x)) = f(2x -3)
= (2x – 3) + 1
= 2x – 2
Therefore, f+g = 3x – 2
f – g = 4 – x
f(g) = 2x – 2