Question

in the figure, TA and TB are the tangents to the circle with the centre O if angle ATB= 80 ° then find the measure of angle ABT ​

Answer 1

Answer: 50 I guess

Step-by-step explanation: it is an isosceles triangle as the tangents will be equal

So angle A and Angle B are equal and 50 degrees

Answer 2

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As we know, tagents from an exeternal point are equal

=> TA = TB

Angles opposite to equal sides are equal,

=> ∠TAB = ∠TBA

Now, let  ∠TBA be x

In triangle TAB

∠TAB+∠TBA+∠ATB = 180° [ Angle sum property of a triangle]

Substuting the angles we get

x + x + 80 = 180

2x + 80 = 180

2x = 100

x = 80°

$\boxed{∠ABT=50°}$