Answer :

The alternate segment theorem (also known as the tangent-chord theorem) states that in any circle, the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.

Therefore by above theorem,

∠BAT = ∠BTP = 72°

Sum of all angles of a triangle = 180°

In ΔABT,

∠ABT + ∠BTA + ∠TAB = 180°

⇒ ∠ABT + 43° + 72° = 180°

⇒ ∠ABT + 115° = 180°

⇒ ∠ABT = 180° – 115°

⇒ ∠ABT = 65°

Hence, ∠ABT = 65°

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