Question

In the given figure, if TP and TQ are tangents to a circle with centre O, so
that ∠POQ = 110°, then ∠PTQ is
(a) 110° (b) 90°
(c) 80° (d) 70°

Answer 1

Answer:

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Step-by-step explanation:

Angle POQ + angle PTQ =180

Hence, anglePTQ=70

Ans-d)7

0°

Answer 2

Answer:

From the question, it is clear that OP is the radius of the circle to the tangent PT and OQ is the radius to the tangents TQ.

So, OP ⊥ PT and TQ ⊥ OQ

∴∠OPT = ∠OQT = 90°

Now, in the quadrilateral POQT, we know that the sum of the interior angles is 360°

So, ∠PTQ+∠POQ+∠OPT+∠OQT = 360°

Now, by putting the respective values we get,

∠PTQ +90°+110°+90° = 360°

∠PTQ = 70°

So, ∠PTQ is 70° which is option B.