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3 problems match “congruent triangles”. Clear

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1. Angle NCB in a triangle ●●●○○ 50 ptsIn $\triangle ABC$, $\angle ABC=50^{\circ}$ and $\angle ACB=20^{\circ}$. Point $N$ is inside $\triangle ABC$ with $\angle NAB=40^{\circ}$ and $\angle NBC=30^{\circ}$. Find the measure of $\angle NCB$ in degrees.
2. Angle in a pentagon with interior point ●●●●○ 100 ptsLet $P$ be a point inside regular pentagon $ABCDE$ such that $\angle PAB=48^{\circ}$ and $\angle PDC=42^{\circ}$. Find $\angle BPC$, in degrees.
3. Angle APC from given cevian angles ●●●●○ 100 pts$P$ is a point inside triangle $ABC$ such that $\angle PBC=30^\circ$, $\angle PBA=8^\circ$ and $\angle PAB=\angle PAC=22^\circ$. Find $\angle APC$, in degrees.