Question

In the figure below, m< ROP = 125°.

Find the measure of the arc RPQ. For the arc RPQ, write two or more complete sentences explaining which theorem or postulate you used to find your answer. Include your equations and calculations in your final answer.

Answer 1

Using supplementary law, QR and SP = 55°.

QOS = 125°

Follow the image below. Simple arithmetic!

Answer 2

The measure of the arc RPQ is 205°

Explanation:

Given the figure in which

m∠ROP=125°

we have to find the measure of the arc RPQ.

As QP is diameter i.e a straight line therefore

∠1 and ∠2 forms a linear pair hence these angles are supplementary.

By supplementary law

∠1+∠2=180°

∠1+125°=180°

∠1=180°-125°=55°

Now we have to find the measure of the arc RPQ i.e

we have to find the measure of ∠2+∠3

By theorem, angles around a point will always add up to 360 degrees.

∴ ∠1+∠2+∠3=360°

55°+∠2+∠3=360°

∠2+∠3=860-55=205°

Hence, the measure of the arc RPQ is 205°