SOLUTION: Find the measures (in degrees) of the remaining angles of trapezoid ABCD if AB ∥ DC and m∠A = 59° and m∠C = 121 m∠B = m∠D =

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Question 1193135: Find the measures (in degrees) of the remaining angles of trapezoid ABCD if AB ∥ DC and m∠A = 59° and m∠C = 121
m∠B =
m∠D =
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

Let's sketch it and see:



Draw DE perpendicular to parallel bases AB and DC.



1. Now since triangle AEB is a right triangle, you can find m∠ADE.
And you know that m∠EDC = 90o, now you can find the measure
of the whole angle at D, namely m∠ADC, which could be called m∠D 
before we drew in DE.

2. Now that you have the measures of all but one of the interior angles, 
use the fact that the sum of the measures of the interior angles of
any quadrilateral is 360o to find m∠B.

Edwin
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Adjacent angles of a trapezoid are supplementary.

Since angles A and C are opposite angles and are supplementary, we know angles B and D have the same measures as angles A and C.

But there is not enough information to know which is which....

ANSWER: In either order, the measures of angles B and D are 59 and 121 degrees.
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