Question

The exterior angle of a regular polygon is one-fifth of its interior angle. How many sides does the polygon have?

Answer 1

Answer:

the sum of the exterior angles of a polygon with n sides is always 360° - for any integer, n. so each of the n exterior angles individually would measure 360n °.

The sum of the interior angles of a polygon with n sides depends on the value of n, (the number of sides). The sum of interior angles is 180(n-2)°, so each interior angle is equal to 180(n−2)n °.

so in the question here, the given information says the following:

360n = 15⋅180(n−2)n

solve for n to find the number of sides.

cross multiply maybe….

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

(n-2) = (2)(5)

n-2 = 10

n= 12.