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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°

Find the measure of angle DEG image of fivesided polygon ABCDE with a ray extending out of each corner the angles formed in corners A B C and D are labeled 115 class=

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ANSWER

[tex]44 \degree[/tex]


EXPLANATION

The sum of the exterior angles of a polygon is
[tex]360 \degree[/tex]


So we sum all the exterior angles to obtain,

[tex] \: < \: DEG +61 + 88 + 52 + 115 = 360 [/tex]


This implies that,

[tex] \: < \: DEG + 316 = 360 [/tex]


We group like terms to obtain,

[tex] \: < \: DEG = 360 - 316[/tex]

This simplifies to,

[tex] \: < \: DEG = 44 \degree[/tex]


Therefore the correct answer is option B.

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