Question

In Figure-2, TP and TQ are tangents drawn to the circle with centre at O
If angle POQ = 115° then angle PTQ is​

Answer 1

Answer:

∠PTQ = 65°

Step-by-step explanation:

∠P = 90°   and ∠Q=90° , ∠O = 115°

In quadrilateral OPTQ ,

sum of opposite angles of a quadrilateral is 180°

∴ ∠O +∠T = 180°

 115 +  ∠T = 180 °

∠ T = 180 - 115 = 65°

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Answer 2

The measure of angle PTQ is 65°

Step-by-step explanation:

here , TP  and TQ are the tangents drawn to a circle with center O

OP ⊥ PT and OQ ⊥TQ

i,e $\angle OPT = \angle OQT = 90^\circ$

given that $\angle POQ = 115^\circ$

then in a quadrilateral TOPQ

sum of all the angles of a quadrilateral is 360°

therefore ,

$\angle OPT+\angle OQT +\angle POQ +\angle PTQ = 360 \\\\90+90+115 +\angle PTQ= 360 \\\\\angle PTQ = 360-295 \\\\\angle PTQ = 65^\circ$

hence , The measure of angle PTQ is 65°

#Learn more:

Two tangent TP and TQ are drawn to a circle with Centre O such that angle tqp=60° then angle opq =

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