Question

Find the measure of Arc vrt

Answer 1

The first step to calculate the measure of the arc is to determine the angle VR. To do that we need to understand that the angles UV, VQ and QR are suplementary, which means that their sum is equal to 180 degrees. So we have:

`\begin{gathered} \measuredangle UV+\measuredangle VQ+\measuredangle QR=180 \\ 54+95+\measuredangle QR=180 \\ 149+\measuredangle QR=180 \\ \measuredangle QR=180-149 \\ \measuredangle QR=31 \end{gathered}`

The angle QR is equal to 31 degrees, with this we can find the angle VR, because it is the sum of VQ and QR.

`\begin{gathered} \measuredangle VR=\measuredangle VQ+\measuredangle QR \\ \measuredangle VR=95+31=126 \end{gathered}`

The arc measure is equal to 126 degrees.