Question

In the given figure TA and TB are the tangents to the circle with center O if angle ATB=80degrees then find the measure of angle ABT

Answer 1

Answer:

In the given figure TA and TB are the tangents to the circle with center O if angle ATB=80° then the measure of angle ABT = 50°

Step-by-step explanation:

∠ATB = 80°

∠ATB + ∠AOB = 180°   ( angle formed by two tangents)

∠AOB = 100°

in Δ OAB

OA = OB = Radius

∠OBA = ∠OAB = x°

∠OBA + ∠OAB + ∠AOB = 180°

x° + x° + 100° = 180°

x° = 40°

∠OBT = 90° (Tangent)

∠OBT = ∠ABT + ∠OBA

=> 90° = ∠ABT + 40°

=> ∠ABT = 50°