SOLUTION: In parallelogram ABCD the measure of angle A is three times that of angle B. What are the measures of C and D?

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Question 830236: In parallelogram ABCD the measure of angle A is three times that of angle B. What are the measures of C and D?
Answer by jim_thompson5910(35256) About Me  (Show Source):
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In parallelogram ABCD the measure of angle A is three times that of angle B. What are the measures of C and D?

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"the measure of angle A is three times that of angle B" ----> A+=+3B

For ALL parallelograms, the adjacent angles are supplementary. So that means the two angles add to 180 degrees

A+B = 180

3B+B = 180 ... plug in A = 3B

4B = 180

B = 180/4

B = 45

A = 3B

A = 3*45

A = 135

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For ALL parallelograms, the opposite angles are congruent (ie equal), which means

A = C

135 = C

C = 135


B = D

45 = D

D = 45

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Summary:

A = 135 degrees
B = 45 degrees
C = 135 degrees
D = 45 degrees