Question

$P$ is a point inside $\Delta ABC$. If $\angle PBA={20}^{\circ },\angle BAC={50}^{\circ }and\angle PCA={35}^{\circ }$, then the measure of $\angle BPC$ is

• A. ${65}^{\circ }$
• B. ${75}^{\circ }$
• C. ${90}^{\circ }$
• D. ${105}^{\circ }$

Answer 1

The correct option is D ${105}^{\circ }$

The sum of all angles in a triangle = 180
$180=\angle BAC+\angle PBA+\angle PBC+\angle PCB+\angle PCA180={50}^0+{20}^0+\angle PBC+\angle PCB+{35}^{0}180=105+\angle PBC+\angle PCB⟹\angle PBC+\angle PCB={75}^0$
In triangle PBC, $180=\angle BPC+\angle PBC+\angle PCB180=\angle BPC+{75}^0⟹\angle BPC={105}^0$