Question

If the measure of arc AC is 140°, what is the measure of angle ABC?

Answer 1

The answer is not 70, my best guess would be 40

Answer 2

Answer: The measure of angle ∠ABC=40°.

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°.