Question

In the diagram shown rays SQ, ST, and SR are drawn so that angle QSR = 105 degrees. If angle QST has a measure that is twice as large as the measure of angle TSR then which of the following is the measure of angle OST?

Answer 1

We have that

`\begin{gathered} m\angle QST+m\angle TSR\text{ = m}\angle QSR \\ m\angle QSR=105 \\ m\angle QST\text{ = 2 (m}\angle TSR) \end{gathered}`

If we replace the second and third equations into the first one we obtain

`\begin{gathered} 2(m\angle TSR)\text{ + m}\angle TSR=105\text{ } \\ 3(m\angle TSR)=105 \\ m\angle TSR\text{ = }35\mathring{} \end{gathered}`

So, since the measure of the angle QST is twice the measure of the angle TSR then we conclude that

`m\angle QST\text{ = 70 degrees}`