Answer: The measure of angle ∠ABC=40°.
Step-by-step explanation:
Since we have given that
Measure of the arc AC = 140°
So, ∠AOC = 140° (Arc angle is equal to central angle)
And we know that "Radius is the perpendicular to the tangent".
∠A=∠C=90°
So, In AOCB,
∠A+∠O+∠C+∠B=360°
90°+140°+90°+∠B=360°
320°+∠B=360°
∠ABC=360°-320°
∠ABC=40°
Hence, The measure of angle ∠ABC=40°.
