Execise 8.3.2
1. Find x in the following figures.
= Three exterior angles 125,125 and x.
We know that, sum of the seterior angles=360.
= 125+125+x=360
= 250+x=360
x =
= So,by linear pair ∠1+∠B=180
= ∠1+90=180°
= ∠1=
Thus,our exterior angles are : x,90°,60°,90°,70°.
We know that
Sum of exterior angles = 360°
= x+90+60+90+70=360
= x=360°-310° =
2. Find the measure of each exterior angle of a regular polygon of.
(i) 9 sides : Exterior angle =
n = Number of sides if regular polygon.
Given,Number of sides of regular Polygon = 9.
Exterior angle= =
(ii) 15 sides : Exterior angle =
n = Number of sides if regular polygon.
Given,Number of sides of regular Polygon = 15.
Exterior angle= =
3. How many sides does a regular polygon have if the measure of an exterior angle is 24°.
= Exterior angle is 24°
= In a regular polygon
Sum of the exterior angles = 360°
Exterior Angle x Number of sides = 360°.
24° x n = 360°
= n = =
4. How many sides does a regular polygon have if each of its interior angles is 165°?
By linear Pair
Interior Angle + Exterior Angle = 180°
= 165° + Exterior Angle = 180°
= Exterior Angle =
5. (a) Is it possible to have a regular polygon with measure of each exterior angle as 22°?
= In a regular Polygon
= Sum of the exterior angles = 360°
= 22° x n = 360°.
= n =
22° external angle is not possible.
(b) Can it be an interior angle of a regular polygon? Why?
= By linear pair,
= Interior Angle + Exterior Angle = 180°.
= 22°+External Angle = 180°.
External Angle =
= In a regular polygon
Sum of the exterior angles = 360°
= 158° x n = 360°.
n= =
Since n cannot be in decimals.
158° external angles is not possible.
- (a) What is the minimum interior angle possible for a regular polygon? Why?
Consider a regular polygon having the least number of sides an equilateral triangle.
We know that the sum of all the angles of a triangle = 180°.
x + x + x = 180°.
3x = 180°.
x =
The minimum interior angle possible for a regular polygon = 60°.
(b) What is the maximum exterior angle possible for a regular polygon?
Consider the interior angle to be 60° since an equilateral triangle is a regular polygon having maximum exterior angle because it consists of the least number of sides.
Exterior angle = 180° - 60° =