Question

The circle below has center T. Suppose that mUV=68° and that UW is tangent to the circle at U. find the following.(a) m

Answer 1

Angle UTV is given: 68°

Since the triangle is isoceles, the other two angles measure the same.

This way,

`\begin{gathered} 68+x+x=180\rightarrow68+2x=180\rightarrow2x=112 \\ \rightarrow x=112 \end{gathered}`

Thereby,

`m\angle TUV=56`

Notice that

`m\angle TUV+m\angle\text{VUW}=90`

Because UW is tangent to the circle

Therefore,

`\begin{gathered} m\angle TUV+m\angle\text{VUW}=90 \\ \rightarrow m\angle\text{VUW}=90-m\angle TUV \\ \rightarrow m\angle\text{VUW}=90-56 \\ \rightarrow m\angle\text{VUW}=34 \end{gathered}`

Answer:

`\begin{gathered} m\angle UTV=68 \\ m\angle VUW=34 \end{gathered}`