Question

R 110° S P In the diagram, O is the centre of the circle. P, Q, R and S are points on the circle. Angle ROP = 110° Calculate the size of angle RSP.​

Answer 1

angle RSP = 125°

Explanation:

You want the measure of inscribed angle RSP that subtends long arc RQP when short arc RP is 110°.

Inscribed angle

The inscribed angle is half the measure of the arc it subtends. That long arc is the difference between 360° and the short arc RSP of 110°.

angle RSP = (1/2)(360° -110°) = 250°/2

angle RSP = 125°

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Additional comment

Angle RSP is the supplement to inscribed angle RQP, which is half the measure of central angle ROP. 180° -(110°/2) = 125° = angle RSP, as above.

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