Question

In the figure below, m ROP = 125°.

Answer 1

The measure of an arc is twice the size of the internal angle.

Answer 2

Answer: Hello!

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.