Question

8. Find the measure of each numbered angle in the figure.​

Answer 1

Answer:

m∠1 = 85°, m∠2 = 85°, m∠3 = 64°, m∠4 = 31°

Step-by-step explanation:

1. Since ∠3 and the angle labeled 64° are vertical, they are congruent, therefore m∠3 = 64°

2. By the same logic, since ∠4 and the angle labeled 31° are vertical, they are also congruent, meaning m∠4 = 31°

3. ∠4, ∠1, and 64° make up 180°, thus a straight line around them, so m∠1 + 31° + 64° = 180° --> m∠1 = 85°

4. ∠1 and ∠2 are vertical, so they are congruent, meaning m∠2 = 85°