PTQ is a tangent to the circle at T, TR=TS and angle RST= 65°. Angle PTS=?.
In triangle TRS , TR=TS therefore angle TRS= angle RST.
Thus , angle TRS=65°.
Now angle STQ is the angle between the tangent PTQ and cord TS.
Therefore angle STQ=angle TRS = 65°.
Tangent PTQ is a straight line , therefore
Angle PTS+angle STQ=180°
Angle PTS+65°=180°
or. angle PTS=180°-65° = 115°. Answer.
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Explanation: