Question

PQ is diameter,PRT and QST are secants. Given angle ROS = 42 find angle RTS

Answer 1

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Answer 2

Diameter = PQ (Given)

Secants = PRT and QST (Given)

Construction - Join the line PS

∠PSQ = 90°

∠SPR = 1/2 ∠ ROS ( Angle at the centre is double as the angle at circumference subtended by the same chord)

= SPT = 1/2 × 42

= 21°

In ΔPST

∠PTS = 90° - ∠SPT

∠ RTS = 90 - 21

= 69

Thus ∠RTS is 69°.