9514 1404 393
Answer:
(a) 15
Step-by-step explanation:
Each of the marked angles is an exterior angle of the polygon. The sum of exterior angles is always 360°. We can use that fact to write the equation.
4x° +77° +59° +6x° +74° = 360° . . . . . an equation to find x
10x + 210 = 360 . . . . . . . . . . . . . . divide by °, collect terms
x + 21 = 36 . . . . . . . . . . . . . . . divide by 10
x = 15 . . . . . . . . . . . . . . . subtract 21
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<em>Comment on the sum of exterior angles</em>
Imagine the figure shrunk smaller and smaller until all of the angle vertices are the same point. You can see that those angles will completely fill the angular space around that central point, so they must have a sum of 360°.
