Question

QUESTION IS IN IMAGE!!! DONT NEED TO SHOW WORK JUST NEED ANSWER!!!!!

Answer 1

Since P is the center of the circle, then the segments PS and PQ are both radii of the circle and have the same measure. Then, the triangle PQS is an isosceles triangle, then, the measures of the angles PQS and QSP must be the same.

Since the sum of the internal angles of a triangle must be equal to 180º, then:

`\begin{gathered} m\angle PQS+m\angle QSP+m\angle SPQ=180º \\ \Rightarrow m\angle PQS+m\angle PQS+113º=180º \\ \Rightarrow2m\angle PQS=180º-113º \\ \Rightarrow2m\angle PQS=67º \\ \Rightarrow m\angle PQS=(67º)/(2) \\ \Rightarrow m\angle PQS=33.5º \end{gathered}`

The measure of RQS is the same as the measure of PQS.

Therefore, the answer is:

`m\angle RQS=33.5º`