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