# The Measure of Each Interior Angle of a Regular Polygon is Five Times the Measure of Its Exterior Angle. Find : - Mathematics

Sum

The measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Find :

(i) measure of each interior angle ;
(ii) measure of each exterior angle and
(iii) number of sides in the polygon.

#### Solution

Let exterior angle = x°

Interior angle = 5x°

x + 5x = 180°

6x = 180°

x = 30°

Each exterior angle = 30°

Each interior angle = 5 x 30° = 150°

Let no. of sides = n

∵ each exterior angle = 360^circ/"n"

30^circ = (360^circ)/"n"

n = (360^circ)/30^circ

n = 12

Hence (i) 150° (ii) 30° (iii) 12

Concept: Regular Polynomial
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#### APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 16 Understanding Shapes
Exercise 16 (B) | Q 8 | Page 184