Question

If the figure, of TP and TQ are two tangents to a circle with centre O, triangle POQ = 110°, then triangle PTQ is equal to​

Answer 1

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°

Answer 2

Answer:

70°

Step-by-step explanation:

PTQO becomes cyclic quadrilateral, therefore opposite angles poq and ptq will add up to 180°. Therefore, angle ptq = 180° - 110° = 70°

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