CPM Homework Help : CCG Problem 7-7

Use the relationships in the diagram at right to find the values of each variable. Name which geometric relationships you used.

Hint:

Refer to the Math Notes box in Lesson 2.1.4 if you need help establishing any angle pair relationship.

Step 1:

Since the highlighted angles are vertical angles, and vertical angles are equal, $37°+a=63°$ .

Step 2:

$∠c$ is an alternate interior angle to $∠a$ . Recall that alternate interior angles are equal.

Step 3:

Use the Triangle Angle Sum Theorem to calculate $b$ : $37°+c+52+b=180°$ .

More Help:

To find $m∠d$ , notice that it is the exterior angle in the small triangle that contains $∠b$ and $52°$ . What relationship do those angles have?

The diagram shows that 63 degrees is the same as 37 degrees + a.