CPM Homework Help : INT1 Problem 8-113

Use the angle relationships in the diagram below to determine the value of each variable. Name which geometric relationships you used.

Step 1:

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

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 $b: 37º + c + 52 + b = 180º$ .

More Help:

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

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