Question

I need help with this problem, 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:

mRP = 125°

mQS = 125°

mPQR = 235°

mRPQ = 305°

Step-by-step explanation:

Given that

• mROP = 125°

• ∠ROP is a central angle

Then:

• measure of arc RP, mRP = mROP = 125°

Given that

• ∠QOS and ∠ROP are vertical angles

Then:

• mQOS = mROP = 125°

• measure of arc QS, mQS = mROP = 125°

Given that

• ∠QOR and ∠SOP are vertical angles

Then:

• mQOR = mSOP

Given that

• The addition of all central angles of a circle is 360°

Then:

mQOS + mROP + mQOR + mSOP = 360°

250° + 2mQOR = 360°

mQOR = (360°- 250°)/2

mQOR = mSOP = 55°

And (QOR and SOP are central angles):

• measure of arc QR, mQR = mQOR = 55°

• measure of arc SP, mSP = mSOP = 55°

Finally:

measure of arc PQR, mPQR = mQOR + mSOP + mQOS = 55° + 55° + 125° = 235°

measure of arc RPQ, mRPQ = mROP + mSOP + mQOS = 125° + 55° + 125° = 305°