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?