Question

In a regular polygon, the ratio of the measure of the exterior angle to the measure of its adjacent interior angle is 1 to 5. How many sides does the polygon have?

Answer 1

Let x be the measure of the exterior angle of the regular polygon.
Then, 5x is the measure of the adjacent interior angle of the polygon.
x + 5x = 180
6x = 180
x = 30
The sum of the exterior angles of a polygon is 360. If each angle has measure 30 and the sum is 360, then there are 360/30 = 12 angles. (and 12 sides) The regular polygon is a regular dodecagon.

Answer 2

thank you so much!