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Geometry

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As shown in the figure, two angle bisectors of $$\triangle ABC$$,$$\overline {BE}$$ and $$\overline {CF}$$, intersect at P. If $$\angle EPF= 111^{\circ}$$, what is $$\angle A$$ in degrees?

Sep 8, 2019

$$\text{Let }\angle A = x, \angle PBC = \angle PBF = y, \angle PCB = \angle PCE = z\\ \begin{cases} x + y +z = 111^{\circ}\\ x+2y+2z = 180^{\circ} \end{cases} \implies y + z = 69^{\circ}\\ x + 69^{\circ} = 111^{\circ}\\ x = 42^{\circ}\\ \angle A = 42^{\circ}$$