NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2

These NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.2

Question 1.
Find x in the following figures.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q1
Solution:
(a) Sum of all the exterior angles of a polygon = 360°
⇒ 125° + 125° + x° = 360°
⇒ 250° + x = 360°
⇒ x = 360° – 250°
⇒ x = 110°

(b) 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) Number of sides (n) = 9
Number of exterior angles = 9
The given polygon is a regular polygon
All the exterior angles are equal
Measure of an exterior angle = \(\frac{360^{\circ}}{9}\) = 40°

(ii) Number of sides of regular polygon = 15
Number of equal exterior angles =15
The sum of all the exterior angles = 360°
The measure of each exterior angle = \(\frac{360^{\circ}}{15}\) = 24°

Question 3.
How many sides does a regular polygon have if the measure of an exterior angle is 24°?
Solution:
For a regular polygon, measure of each angle is equal
Sum of all the exterior angles = 360°
Measure of an exterior angle = 24°
Number of sides = \(\frac{360^{\circ}}{24^{\circ}}\) = 15
Thus, there are 15 sides of the regular polygon.

Question 4.
How many sides does a regular polygon have if each of its interior angles is 165°?
Solution:
The given polygon is a regular polygon.
Each interior angle = 165°
Each exterior angle =180° – 165° = 15°
Number of sides = \(\frac{360^{\circ}}{15^{\circ}}\) = 24
Thus, there are 24 sides of the polygon.

Question 5.
(a) Is it possible to have a regular polygon with measure of each exterior angle 22°?
(b) Can it be an interior angle of a regular polygon? Why?
Solution:
(a) Each exterior angle = 22°
∴ Number of sides = \(\frac{360^{\circ}}{22^{\circ}}=\frac{180^{\circ}}{11^{\circ}}\)
If it is a regular polygon, then its number of sides must be a whole number.
Here \(\frac{180^{\circ}}{11^{\circ}}\) is not a whole number.
∴ 22° cannot be an exterior angle of a regular polygon.

(b) If 22° is an interior angle, then
(180° – 22°) = 158° is an exterior angle.
∴ Number of sides = \(\frac{360^{\circ}}{158^{\circ}}=\frac{180^{\circ}}{79^{\circ}}\)
\(\frac{180^{\circ}}{79^{\circ}}\) is not a whole number
∴ 22° cannot be an interior angle of a regular polygon.

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) The minimum number of sides of a polygon = 3
The regular polygon of 3 sides is an equilateral triangle.
∴ Each interior angle of an equilateral triangle is 60°.

(b) The sum of an exterior angle and its corresponding interior angle is 180°.
Minimum interior angle of a regular polygon is 60°.
∴ The maximum exterior angle of a regular polygon = 180° – 60° = 120°

error: Content is protected !!