Question

How many sides does a regular

polygon have if one interior
angle measures 135°?
n = [?]
Hint: The measure of each interior angle
(n-2)180
in a regular n-gon is
n

Answer 1

8

Explanation:

In a regular polygon of n sides, each interior angle measures (n - 2)180/n.

Here, each interior angle measures 135°.

We set the expression equal to 135°, and solve for n, the number of sides.

(n - 2)180/n = 135

Multiply both sides by n.

(n - 2)180 = 135n

180(n - 2) = 135n

Distribute 180 on the left side.

180n - 360 = 135n

Add 360 to both sides.

180n = 135n + 360

Subtract 135n from both sides.

45n = 360

Divide both sides by 45.

n = 360/45

n = 8