CIRCLES C11

Find the value of <PRN in the figure below.

Solution

<PMR = <PNR ( angles subtended by the same arc are equal)

<PMR = 68⁰

so, <PMN = 68⁰ + 36⁰

                = 104⁰

<PMN + <PRN = 180⁰ (opposite angles in a cyclic quadrilateral add up to 180)

∴ 104⁰ + <PRN = 180⁰

∴  <PRN = 180⁰ - 104⁰

∴  <PRN = 76⁰