Question

The ratio between an exterior angle and the interior angle of a regular polygon is 1 : 2. Find: (a) the measure of each exterior angle. (b) the measure of each interior angle. (c) the number of sides in the polygon.

Answer 1

Step-by-step explanation:

Given that ratio between an exterior angle and the interior angle =1:2

we know that measure of an interior angle =(n-2)(180/n) and the measures of an exterior angle = (370/n )

1/2 =( 360/n ) / ( n-2) (180/n)

1/2= (360/n) /n/ (n-2)* 180

1/2= (360/n) /n (180n -360)

1/2 = (360) /(180(n-2))

1/2= 2/(n-2)

1(n-2) =2* 2

n-2 = 4

n=8

= The number of side in the polygon are 8

The measure of each exterior angle =360/(n)

=360/8

=45

The measure of each exterior angle are 45

The measure of each interior angle =180-45

= 135

(a). The measure of each exterior angle is 8

(b). The measure of each interior angle is 135

(c).The number of sides in the polygon is 8