Question 1069216: In a quadrilateral ABCD, the interior angles marked A, B, C, and D are in the ratio 6:7:8:9. Find the greatest interior angle
and the greatest exterior angle.
Answer by ikleyn(53763)   (Show Source):
You can put this solution on YOUR website! .
In a quadrilateral ABCD, the interior angles marked A, B, C, and D are in the ratio 6:7:8:9. Find the greatest interior angle
and the greatest exterior angle.
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The first phrase of the condition means that there is a common measure angle "x" such that
A = 6x, B = 7x, C = 8x, and D = 9x.
Since the sum of interior angles of any quadrilateral is 360 degs, you have this equation
6x + 7x + 8x + 9x = 360, or
30x = 360, hence, x =  = 12 degs.
Then the greatest interior angle is 9x = 9*12 = 108 degs.
Answer. The greatest interior angle is D = 108 degs.
The greatest exterior angle is 180 - 6x = 180 - 72 = 108 degs.
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