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Does anyone mind giving me a hand answering this question?

Does anyone mind giving me a hand answering this question?-example-1
User Ojunk
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1 Answer

14 votes
14 votes

Answer:

A. x = 4

B. ∠C = 80°

Explanation:

A.

The sum of interior angles in a pentagon is 540°. We can write an equation for the sum of angles using this fact. Clockwise from lower left, we have ...

140° +(20x)° +100° +(16x +16)° +(160 -5x)° = 540°

31x +416° = 540° . . . . . . collect terms

31x = 124° . . . . . . . . . . subtract 416°

x = 4

__

B.

The measure of angle C is found by substituting the value of x into the given expression for angle C.

(16x +16)° = (16(4) +16)° = 80°

Angle C is 80°.

_____

Additional comment

It can be useful to remember that the sum of interior angles of an n-gon is ...

(180°)(n -2)

This can be derived from the fact that the sum of exterior angles is always 360°.

These relations apply to convex polygons. YMMV when there are reflex angles or when sides cross each other.

User Guy Yogev
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3.1k points