Question

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 (iii)number of sides in the polygon

Answer 1

hey!!! friend Ur answer goes like this...
let x be the exterior angle and 5x be the interior angle
we know 5x+x=180 so x is 30°
i)so measure of each interior angle is 30*5=150°
ii)and measure of each interior angle is 30°
iii) we know no. of sides in a polygon=360°÷exterior angle
So no. of sides in this polygon is 360°÷30=12 sides..

Answer 2

Answer:

(i) 150°  (ii) 30° (iii)12

Step-by-step explanation:

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°/n

30° = 360°/n

n = 360°/30°

n = 12

Hence  (i) 150°  (ii) 30° (iii)12