Q. 54.4( 9 Votes )

If TP and TQ are

Answer :

Given:


POQ = 110°



Property 1: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.


Property 2: Sum of all angles of a quadrilateral = 360°.


By property 1,


TPO = 90°


TQO = 90°


By property 2,


POQ + TPO + TQO + PTQ = 360°


PTQ = 360° - POQ + TPO + TQO


PTQ = 360° - (110° + 90° + 90°)


PTQ = 360° - 290°


PTQ = 70°


Hence, PTQ = 70°

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