Question

55MAssuming that angles that appear to be central angles are central angles, then:mPM=mMR=mRQmQs:: 35°:: 55°:: 90°:: 125°

Answer 1

We are given the measure of the angle subtended by arc PS as 55 degrees.

Solution:

The measure of arc PM

`\bar{\text{mPM}}=90^0\text{ (given)}`

The measure of arc MR

`\begin{gathered} \bar{\text{mMR}}+90^0+55^{\text{ 0}}=180^0\text{ (angles in a straight line)} \\ \bar{mMR}=180^0-90^0-55^0 \\ =35^0 \end{gathered}`

The measure of arc RQ

`\bar{\text{mRQ}}=55^0\text{ (Vertically opposite angles)}`

The measure of arc QS

`\begin{gathered} \bar{\text{mQS}}+55^0=180^0\text{ (} \\ \bar{\text{mQS}}=180^{0\text{ }}-55^0 \\ =125^0 \end{gathered}`