WAEC Mathematics Question 2015 ( Essay Question Three 3b )

3b. The diagram shows a circle PQRS with centre O, < UQR = 68°, < TPS = 74° and < QSR = 40°. Calculate the value of < PRS.

SOLUTION

From the diagram above, we deduce that PSR = 68° (The Interior Angle of a Cyclic Quadrilateral = Opposite Exterior Angle)

Therefore, ° + 40° = 68°

                 ° = 68 - 40

                 ° = 28°

Since ° = 28°, we can conclude that PRQ = 28° (Angles in the same segment are equal)

Also, SRQ = 74° (Interior Angles of  a Cyclic Quadrilateral = Opposite Exterior Angle)

Therefore, to obtain PRS, we have;

PRS = 74° - 28°

PRS = 46°  ANSWER

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