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In rectangle ABCD below, we have DP = PC and < BAC = 21 degrees. Find the number of degrees in < QDA + < PDC.

 

 Feb 4, 2022
 #1
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Since angle(BAC) = 21o     --->     angle(QAD) = 69o     --->     angle(QDA) = 21o.

 Feb 5, 2022
 #2
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Since triangle PDC is an isosceles triangle, and AB is parallel to DC because it is a rectangle, then that means angle DCP is congruent to angle BAC. So angle PCD is 21*. Angle PDC is also 21*.

 

Angle DAQ is 90 - 21 = 69*. So QDA is 180-90-69 = 21 degrees. Since we are looking for the sum of angles PDC and angle QDA, the answer is 42*.

 

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 Feb 5, 2022

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