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# triangle

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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