Question

Using Vertical Angles to find Unknown Values What is m

Answer 1

Vertical angles measure the same, then angle TRS is equal to VRW, and angle SRW is equal to TRV.

Also, the addition of these 4 angles is equal to 360°.

First, we need to find TRS and VRW:

`\begin{gathered} \measuredangle TRS=\measuredangle VRW \\ 2x+18=3x \\ 18=3x-2x \\ 18=x \\ \\ \measuredangle VRW=3*18=54\degree \\ \measuredangle TRS=54\degree \end{gathered}`

Now, the addition of the 4 angles is given by:

`\begin{gathered} \measuredangle TRS+\measuredangle VRW+\measuredangle TRV+\measuredangle SRW=360\degree \\ 54\degree+54\degree+\measuredangle TRV+\measuredangle SRW=360\degree \\ \measuredangle TRV+\measuredangle SRW=360\degree-54\degree-54\degree \\ \measuredangle TRV+\measuredangle SRW=252\degree \end{gathered}`

Also TRV=SRW, so by replacing this:

`\begin{gathered} \measuredangle SRW+\measuredangle SRW=252\degree \\ 2\measuredangle SRW=252\degree \\ \measuredangle SRW=(252\degree)/(2) \\ \\ \measuredangle SRW=126\degree \end{gathered}`

The m