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3 problems match “angle chasing”. Clear

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1. Angle in a regular pentagon ●●○○○ 20 ptsIn a regular pentagon $PQRST$, find the measure of $\angle PRS$ in degrees.
2. Angle in pentagon with inner triangle ●●○○○ 20 ptsIn a regular pentagon $ABCDE$, an equilateral triangle $ABM$ is drawn so that $M$ lies inside the pentagon. Determine the size of the angle $BCM$ in degrees.
3. 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.