CPM Homework Help : CCA2 Problem 4-103

Find the measure of $∠CPM$ in the diagram below. List any sub-problems that were necessary to solve this problem.

Line segment, p, b, intersects, line segment, c, a, at point, m, labeled as follows: Segments, p, c, & a, b, marked with double arrows, angle c, 4, x, minus 3, y, angle a, 65 degrees, angle p, m, c, 2, x, + 3, y, angle a, m, b, 3, x, minus, y.

Hint:

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

Hint 2:

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?

Hint 3:

$65=4x−3y$
$3x−y=2x+3y$

More Help:

How can you find the measure of the third angle?

Step 1:

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

Step 2:

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

Answer:

$∠CPM=60°$