CPM Homework Help : INT3 Problem 8-14

What is the measure of $∠CPM$ in the diagram at right? List any subproblems that were necessary to solve this problem.

Hint:

Recall the angle relationship between vertical angles.
Can you isolate one variable on one side of the equation?

More Help:

If lines $CP$ and $AB$ are parallel, then what is true about angles $C$ and $A$ ?

Step:

Solve the system:
$2x + 3y = 3x − y$
$4x − 3y = 65^\circ$

Once you know the values of $x$ and $y$ , determine the angles in the triangle.

Answer:

$60^\circ$

Line segments, C A, &, P B, intersect at a point labeled, M, with segments from, C, to, P, & from, A, to, B, creating 2 triangles with a shared vertex, labeled as follows: Sides, C P, & A B, each have 2 arrows, angle, C, labeled 4 x minus 3 y, angle, P M C labeled, 2 x + 3 y, angle A, 65 degrees, angle A M B, 3 x minus y.