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In trapezoid $ABCD$, sides $\overline{AB}$ and $\overline{CD}$ are parallel,$\angle A = 2\angle D$ , and 

$\angle C = 3\angle B$. Find $\angle B$.

 Apr 16, 2021
 #1
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By properties of trapzoids, angle C = 90 degrees, so angle B = 30 degrees.

 Apr 16, 2021
 #2
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The properties of the trapezoid are as follows:

The bases are parallel by definition.

Each lower base angle is supplementary to the upper base angle on the same side.

 

So, angle a + angle d = 180

         angle a = 2d    substitute

              2d +d = 180       d= 60

    a= 2d = 120 degrees                                    This assumes your trapezoid is labeled    A            B

                                                                                                                                          D                      C

 

 

Hope this helps~Hannah

 Apr 16, 2021
 #3
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Angles  B  and C  are  supplementary

 

So

 

B +  C  =  180

 

B +  3B  =  180

 

4B  =  180

 

B  =180 / 4   =   45  ( degrees  )

 

cool cool cool

 Apr 16, 2021

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