Question

Find the difference between the measures of arc ST and arc RQ.

Answer 1

We are asked to determine the difference between arcST and Ar RQ. To do that we will use the fact that the sum of arc RS and arc ST is 180 degrees, that is:

`a\text{rc }RS+\text{arc }ST=180,(1)`

We also have that the sum of arc RQ and arc QT is 180, therefore:

`\text{arc RQ+arc QT=180,(2)}`

Now w subtract equation (2) from equation (1):

`\begin{gathered} a\text{rc }RS+\text{arc }ST-\text{arc RQ-arc QT}=180-180 \\ a\text{rc }RS+\text{arc }ST-\text{arc RQ-arc QT}=0 \end{gathered}`

Now we solve for the difference that we require:

`\text{arc }ST-\text{arc RQ}=\text{arc QT-}a\text{rc }RS`

The measure of arcQT is double the measure of the 71 degrees, therefore:

`\text{arq QT=2(71)=}142`

Now we replace the values:

`\begin{gathered} \text{arc }ST-\text{arc RQ}=142\text{-}46 \\ \text{arc }ST-\text{arc RQ}=96 \end{gathered}`

Therefore, the difference is 96 degrees.