Question

In the figure below, m ROP = 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.

Answer 1

The figure given above shows us a circle with a couple of lines intersecting certain points on it. So if we divide the circle into two, then we have a semi circle with an angle of 180° on its vertical side. Since ∠ROP = 125°, then subtract 180° to 125° and you will get ∠POS = 55°. ∠POS is also equal to ∠QOR. And ∠ROP = ∠QOS.