Question

I need help with this question, if anyone could help ASAP, that would be much appreciated. In the figure below, mROP = 125° Find the measure of each arc. For each arc, 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. find mRP, MQS, MPQR, and MRPQ

Answer 1

Answer:The measure of the arc RPQ is 205°

Step-by-step 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°