Question

The ratio of an interior angle to an exterior angle of an n-sided regular polygon is 13 : 2. Find the value of n.​

Answer 1

Answer

The sum of the internal and external angle is 180°. With the ratio of internal to external angles of 13:2, there exists a common multiplier, a.

(13+2)a =180 15a=180. a=180/15 a=12.

The internal angle is 13•12 = 156°

The external angle = 2•12= 24°. 156+24=180 ✓

When regular polygon is segmented into isosceles triangles, with vertices at the center. The sum of the central angles = 360° and the value of each central angle equals the external angle (24°).

So 360/24= 15. The polygon was divided into 15 triangles, and therefore the polygon has 15 sides (and is called a pentadecagon, or a 15-gon.)