Question

In circle Q with the measure of arc ⌢=118∘PR⌢ =118 ∘ , find m∠PQRm∠PQ

Answer 1

Explanation

We are given the measure of arc PR = 118°.

We are required to find m∠PQR.

We know that an arc measure is an angle the arc makes at the center of a circle. Therefore, we have:

$\begin{gathered} obtuse\text{ }m\angle PQR=118\degree \\ obtuse\text{ }m\angle PQR+reflex\text{ }m\angle PQR=360\degree\text{ }\lbrace angles\text{ }at\text{ }a\text{ }point\rbrace \\ reflex\text{ }m\angle PQR=360\degree-obtuse\text{ }m\angle PQR \\ reflex\text{ }m\angle PQR=360\degree-118\degree \\ reflex\text{ }m\angle PQR=242\degree \end{gathered}$

Hence, the answer is:

$\begin{gathered} obtuse\text{ }m\angle PQR=118\degree \\ reflex\text{ }m\angle PQR=242\degree \end{gathered}$

But since Q is the measure of the angle, then the final answer is 118°.