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The trisectors of angles B and $C$ of scalene triangle ABC meet at points P and Q, as shown. Angle A measures 35 degrees and angle QBP measures 12 degrees. What is the measure of angle BPC?

 

 Jul 22, 2022
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Note that \(\angle B = 3 \times \angle QBP = 3 \times 12^\circ = 36^ \circ\)

 

This means that \(\angle C = 180 - 36 - 35 = 109\)

 

So, \(\angle PCB = {109^ \circ \over 3} = 33^ \circ\)

 

But, recall that \(\angle PBC = \angle QBP = 12\)

 

This means that \(\angle BPC = 180 - \angle PBC - \angle QBP = 180 - 33 - 12 = \color{brown}\boxed{135^\circ}\)

 Jul 23, 2022

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