Question

the ratio between an exterior angle and the interior angle of a regular polygon is 1:5 1)the measure of each exterior angle 2) the measure of each interior angle 3)the number of sides in the polygon

Answer 1

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!

Answer 2

Answer:

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). n = 12. Therefore the number of sides in the polygon = 12.