## MP Board Class 8th Maths Solutions Chapter 3 Understanding Quadrilaterals Ex 3.2

Question 1.

Find x in the following figures.

Solution:

(a) Sum of the measures of the exterior angles of any polygon is 360°.

∴ 125° + 125° + x = 360°

⇒ 250° + x = 360°

⇒ x = 360° – 250° ⇒ x = 110°.

(b) Since, sum of the exterior angles of any polygon is 360°.

∴ x + 90° + 60° + 90° + 70° = 360°

⇒ x + 310° = 360° => x = 360° – 310°

∴ x = 50°.

Question 2.

Find the measure of each exterior angle of a regular polygon of

(i) 9 sides

(ii) 15 sides.

Solution:

(i) Let each exterior angle of a regular polygon who has 9 sides is equal to x.

Sum of exterior angles of any polygon is 360°.

Thus each exterior angle of a regular polygon of 9 sides is 40°.

(ii) Let each exterior angle of a regular polygon who has 15 sides is x.

Sum of all exterior angles of a polygon is 360°.

Thus each exterior angle of a regular polygon of 15 sides is 24°.

Question 3.

How many sides does a regular polygon have if the measure of an exterior angle is 24°?

Solution:

Total measure of all exterior angles = 360°

Measure of each exterior angle = 24°

Therefore, the number of sides = \(\frac{360^{\circ}}{24^{\circ}}\)

= 15

The polygon has 15 sides.

Question 4.

How many sides does a regular polygon have if each of its interior angles is 165°?

Solution:

Total measure of all exterior angles = 360°

Measure of each interior angle = 165°

Measure of each exterior angle = 180° – 165°

= 15°

Therefore, number of sides = \(\frac{360^{\circ}}{15^{\circ}}\) = 24

Question 5.

(a) Is it possible to have a regular polygon with measure of each exterior angle as 22°?

(b) Can it be an interior angle of a regular polygon? Why ?

Solution:

(a) No, because 22° is not a divisor of 360°.

(b) No, because each interior angle is 180° – 22° = 158°, which is not a divisor of 360°.

Question 6.

(a) What is the minimum interior angle possible for a regular polygon? Why?

(b) What is the maximum exterior angle possible for a regular polygon?

Solution:

(a) Since each angle of an equilateral triangle is 60°.

And equilateral triangle is a regular polygon.

∴ Minimum interior angle is 60° for a regular polygon.

(b) Since minimum interior angle of a regular polygon is 60°.

∴ Each exterior angle of a regular polygon = 180° – 60° = 120°.

∴ Possible maximum exterior angle of a regular polygon is 120°.