The circle shown below has AB and BC as its tangents. If the measure of arc AC is 130°, what is the measure of angle ABC?

Solution:

The measure of the external angle is the semi difference of the arc it covers.

Here it covers the arc AC and arc ABC.

It is given that

AB and BC are the tangents, the AC arc measures 130°

Based on the theorems on circle

360° = arc AC + arc ABC

360° = 130° + arc ABC

arc ABC = 230°

We know that

∠ABC = 1/2 (230 - 120)

∠ABC = 1/2 (110)

∠ABC = 55°

Therefore, the measure of angle ABC is 55°.

The circle shown below has AB and BC as its tangents. If the measure of arc AC is 130°, what is the measure of angle ABC?

Summary:

The circle shown below has AB and BC as its tangents. If the measure of arc AC is 130°, the measure of angle ABC is 55°.