Question

PLS HELP ASAP 100 POINTS

Find the measure of ∠YOZ by answering the questions.
1. Find the measure of ∠WOV. Which angle relationship did you use? (3 points)
2. Now find the measure of ∠YOZ. Which angle relationship did you use?
3. Check your answer by using another strategy to find the measure of ∠YOZ. Describe your strategy, and show that it gives the same measure for ∠YOZ. (4 points)

Answer 1

1. 60°
2. 60°, vertical angles
3. 60°, measure of a straight angle

Explanation:

Given right angle XOV and 30° angle XOW, you want to know the measure of angle WOV. You also want to find the measure of angle YOZ, which is opposite angle VOW, where XOY is a right angle, and WOZ is a straight angle.

1. WOV

The angle addition theorem tells you that ...

∠XOW +∠WOV = ∠XOV

Angle XOV is given as a right angle, and angle XOW is shown as 30°, so we have ...

30° +∠WOV = 90°

∠WOV = 60° . . . . . . . . . subtract 30° from both sides

Angle WOV is 60° using the angle addition theorem.

2. YOZ

Rays OY and OV are opposite rays, as are rays OZ and OW. This means angles YOZ and VOW are vertical angles, hence congruent.

∠YOZ = ∠WOV = 60°

Angle YOZ is 60° using the congruence of vertical angles.

3. YOZ another way

As in part 2, angle WOZ is a straight angle, so measures 180°. The angle addition theorem tells you this is the sum of its parts:

∠ZOY +∠YOX +∠XOW = ∠ZOW

∠ZOY +90° +30° = 180°

∠ZOY = 60° . . . . . . . . . . . . . subtract 120° from both sides

Angle YOZ is 60° using the measure of a straight angle.

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