Question

Oues- The ratio between an exterior angle and the interior angle of a regular polygon is
1:5. Find

(i) the measure of each exterior angle

(ii) the measure of each interior angle

(iii) the number of sides in the polygon.​

it is of Math's ..

Answer 1

Explanation:

Given that ratio between an exterior angle and the interior angle = 1:5.

We know that measure of an interior angle = (n - 2)(180/n) and the measure of an exterior angle = (360/n).

1/5 = (360/n) / (n - 2)(180/n)

1/5 = (360/n) / n/(n - 2) * 180

1/5 = (360/n) / n(180n - 360)

1/5 = (360)/(180(n - 2))

1/5 = 2/(n - 2)

1(n - 2) = 5 * 2

n - 2 = 10

n = 12.

Therefore the number of sides in the polygon = 12.

(1) Therefore the measure of each exterior angle = 360/(n)

= 360/12

= 30.

(2) Therefore the measure of each interior angle = 180 - 30

= 150.

Hope this helps!