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.

In the figure, Q and P are on opposite ends of the circle, and the same is for R and S, which means that the line that connects Q and P, or R and S, divides the circle in two equal halves. From this, we know that the angle between QoP is 180°, and the same for the angle RoS = 180°.

We also know that the angle RoP = 125°, then the angle between Q and R is the same as the angle between Q and P minus the angle between R and P.

this is : QoR = QoP - RoP = 180° - 125° = 55°

then QoR and RoP are supplementary angles, wich means that the addition adds up to 180°.

And is easy to see that the angles SoQ and PoS are reflexes of RoP and QoR respectively, then:

SoQ = 125° and PoS = 55°, where this angles also are supplementary.

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.

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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.