### Home > CC4 > Chapter 8 > Lesson 8.2.2 > Problem 8-113

8-113.

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

Since the highlighted angles are vertical angles, and vertical angles are equal,

37° + *a* = 63°.

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

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

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?