Question

The measure of an exterior angle of a regular polygon is given below. Find the measure of an interior angle. Then find the number of sides.
45
Question content area bottom
Part 1
What is the measure of an interior​ angle?
A.
105​°
B.
55​°
C.
135​°
D.
155​°
How many sides does the polygon​ have?
A.
5
B.
6
C.
8
D.
10
What is the measure of an interior angle?How many sides does the polygon have?How many sides does the polygon have?

Answer 1

The measure of an exterior angle of a regular polygon is equal to 180 degrees minus the measure of the corresponding interior angle. So, the measure of the interior angle is 180 - 45 = 135 degrees.

To find the number of sides of the regular polygon, we use the formula for finding the interior angle of a regular polygon: Interior angle = 180(n-2)/n, where n is the number of sides.

Setting the interior angle to 135 degrees, we can solve for n:
135 = 180(n-2)/n
135n = 180n - 360
45n = 360
n = 8

Therefore, the measure of an interior angle is 135 degrees and the regular polygon has 8 sides.

The correct answers are:
- What is the measure of an interior angle? C. 135°
- How many sides does the polygon have? C. 8