Question

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Answer 1

Given:

m∠SPQ = 113 degrees

Let's find the measure of angle RQS, m∠RQS.

By applying the angle-arc relationship, we have:

m∠SPQ = measure of arc SQ = 113 degrees.

Since RQ is the diameter, measure of arc RQ = 180 degrees.

Now, let's find the measure of arc RS:

measure of arc RS = 360 - arc SQ - arc RQ

measure of arc RS = 360 - 113 - 180 = 67 degrees.

To find the m∠RQS, apply angle-arc relationship:

`\begin{gathered} m∠RQS=(1)/(2)arcRS \\ \\ m∠RQS=(1)/(2)*67 \\ \\ m∠RQS=33.5^o \end{gathered}`

Therefore, the measure of angle RQS is 33.5 degrees.

ANSWER:

m∠RQS = 33.5°