SOLUTION: I need help understanding and setting up this problem: The exterior angles of a convex pentagon measures (18x+12) , 16x, (8x+6), (10x-12), and (5x+12). Determine the measure of th

Question 835311: I need help understanding and setting up this problem:
The exterior angles of a convex pentagon measures (18x+12) , 16x, (8x+6), (10x-12), and (5x+12). Determine the measure of the largest interior angle
Answer by reviewermath(1029) (Show Source): You can put this solution on YOUR website!
Q:
The exterior angles of a convex pentagon measures (18x+12) , 16x, (8x+6), (10x-12), and (5x+12). Determine the measure of the largest interior angle
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A:
(18x+12) + 16x + (8x+6) + (10x-12) + (5x+12) = 360
57x + 18 = 360
x = (360 - 18)/57 = 6
Therefore,
18x+12 = 18(6)+12 = 120 degrees
16x = 16(6) = 96 degrees
8x + 6 = 8(6) + 6 = 54 degrees
10x - 12 = 10(6) - 12 = 48 degrees
5x + 12 = 5(6) + 12 = 42 degrees
The smallest exterior angle measures 42 degrees.
Therefore, the largest interior angle measures 180 - 42 = 138 degrees
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