SOLUTION: Three of the interior angle measures of a trapezoid are in the ratio 3:5:7. What is the sum of all the possible measures of the fourth interior angle?

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Question 1105740: Three of the interior angle measures of a trapezoid are in the ratio 3:5:7. What is the sum of all the possible measures of the fourth interior angle?
Answer by greenestamps(13203) About Me  (Show Source):
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The sum of the measures of the angles of a trapezoid is 360 degrees.

If the trapezoid is ABCD with bases BC and AD, then the sum of the measures of angles A and B is 180 degrees, and the sum of the measures of angles C and D is 180 degrees.

There are three cases for the problem....

(1) Angles A and B are 3x and 5x; that makes the other two angles 7x and x.
7x%2Bx+=+8x+=+180 --> x = 22.5; the fourth angle is 22.5 degrees.

(2) Angles A and B are 3x and 7x; that makes the other two angles 5x and 5x.
5x%2B5x+=+10x+=+180 --> x = 18; the fourth angle is 5x = 90 degrees.
(3) Angles A and B are 5x and 7x; that makes the other two angles 3x and 9x.
3x%2B9x+=+12x+=+180 --> x = 15; the fourth angle is 9x = 135 degrees.