Question

Four interior angles of a pentagon measure 85°, 90°, 95°, and 110°. What is the smallest measure of the pentagon's exterior angles?
A 5°
B 20°
C 70°
D 85°

Answer 1

An interior and exterior angle add up to 180 degrees.
+
The sum of all the angles in a pentagon is 540 degrees, using that find the missing angle:
85+90+95+110=380
540-380=160

Then, find the exterior angle measure for 160 degrees (160 is interior):
180-160=20

The answer is B) 20

Answer 2

The smallest measure of the exterior angle of a pentagon with interior angles of 85°, 90°, 95°, and 110° is 20 degrees.

What is a pentagon?

Pentagons are polygons with 5 sides.

The sum of interior angles of a pentagon is as follows:

(n - 2)180

where

• n = number of sides

Therefore,

180(5 - 2) = 180(3) = 540 degrees.

Hence, the last interior angle can be found as follows:

85 + 90 + 95 + 110 + x = 540

x = 540 - 380

x = 160

exterior angle  = 180 - 160(interior angle)

exterior angle  = 20°

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