Question

Find the measure of angle DEG.

image of five-sided polygon ABCDE with a ray extending out of each corner; the angles formed in corners A, B, C, and D are labeled 115 degrees, 52 degrees, 88 degrees, and 61 degrees respectively; the fifth corner forms angle DEG

65°

44°

105°

72°

Answer 1

ANSWER


`44 \degree`


Step-by-step explanation

The sum of the exterior angles of a polygon is

`360 \degree`


So we sum all the exterior angles to obtain,


`\: < \: DEG +61 + 88 + 52 + 115 = 360`


This implies that,


`\: < \: DEG + 316 = 360`


We group like terms to obtain,


`\: < \: DEG = 360 - 316`

This simplifies to,


`\: < \: DEG = 44 \degree`


Therefore the correct answer is option B.