### Home > A2C > Chapter 5 > Lesson 5.2.4 > Problem5-101

5-101.

Find the measure of $∠CPM$ in the diagram.

List any subproblems that were necessary to solve this problem.

$\text{Notice that }\overline{AB} \text{ and }\overline{CP} \text{ are parallel.}$

Remember geometric angle relationships.
If the lines are parallel, what must be true about the alternate interior angles?
What is always true about vertical angles?

$65 = 4x − 3y\\3x − y = 2x + 3y$

How can you find the measure of the third angle?

Write and solve a system of equations based on the properties.

Once you find x and y, find the measures of the angles in ΔCPM.

$∠CPM = 60°$