Answer: 155 degrees
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Explanation:
Angle B = 57 in the diagram is adjacent to angle ABC. The two supplementary angles add up to 180. This means angle ABC must be 180-57 = 123. Note how 57+123 = 180.
Line L is parallel to line M which means angle B = 57 is congruent to angle EAB because they are alternate interior angles.
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Focus on the pentagon ABCDE
We have the following interior angles
- A = 57 (aka angle EAB found earlier)
- B = 123 (aka angle ABC found earlier)
- C = 115
- D = unknown (what we want to solve for, since it's angle CDE)
- E = 90
For any pentagon, the interior angles always add to 540 degrees. Use the formula 180(n-2) and plug in n = 5 to get 540.
So we'll add up angles A through E and set that sum equal to 540
From there, we solve for D.
A+B+C+D+E = 540
57+123+115+D+90 = 540
D+385 = 540
D = 540-385
D = 155 degrees is the measure of angle CDE
