Question

In the Figure, PT is a tangent to a circle. If m(∠BTA) = 45° and m(∠PTB) = 70°. Find m(∠ABT). 

Answer 1

∠ ATP = ∠ PTB - ∠ BTA
= 70° - 45°  = 25° 
∴ ∠ ABT = ∠ ATP      ...(Angles are in alternate segments)
⇒ ∠ ABT = 25°.