Question

Find the measure of ∠YOZ by answering the questions.1. Find the measure of ∠WOV. Which angle relationship did you use?2. Now find the measure of ∠YOZ. Which angle relationship did you use?

Answer 1

1.-First, notice that angle WOV and angle WOX are complementary, this means that we have the following equation:

`\measuredangle WOV+\measuredangle WOX=90`

since the measure of angle WOX is 30 degrees, we have the following:

`\begin{gathered} \measuredangle WOV+30=90 \\ \Rightarrow\measuredangle WOV=90-30=60 \\ \measuredangle WOV=60\degree \end{gathered}`

2.- To find the measure of angle YOZ, we can see that it is vertical with angle WOV, thus, we have:

`\begin{gathered} \measuredangle YOZ=\measuredangle WOV=60\degree \\ \Rightarrow\measuredangle YOZ=60\degree \end{gathered}`

therefore, the measure of angle YOZ is 60 degrees since it is vertical with angle WOV