Question

The circle shown below has AB and BC as its tangents: AB and BC are two tangents to a circle which intersect outside the circle at a point B. If the measure of arc AC is 130°, what is the measure of angle ABC? (1 point) 55° 50° 60° 65°

Answer 1

he picture in the attached figure

we know that

The measure of the external angle is the semidifference of the arcs that it covers.

so

the arcs that it covers are

arc AC and arc ABC

We have

AB and BC as its tangents

the measure of arc AC is $130$°

In addition, a circle has $360$ degrees by definition

so

$360$°= arc AC + arc ABC

$360$°= $130$° + arc ABC

arc ABC= $360$°- $130$°= $230$°

Then

Angle ABC = $\frac{1}{2}*(230-130)$

Angle ABC= $50$°

therefore

the answer is

Angle ABC= $50$°

Answer 2

Based on tangent theorem, the measure of angle ABC is: 50°.

Tangent Theorem

• Where two tangents in intersect to form an angle outside a circle, the angle formed outside the circle = 1/2(difference between major arc and minor arc.)

Thus:

m∠ABC = 1/2(measure of arc ABC - measure of arc AC)

Measure of arc ABC = 360 - 130 = 230°

Measure of arc AC = 130° (given)

Therefore:

m∠ABC = 1/2(230 - 130)

m∠ABC = 50°

Therefore, based on tangent theorem, the measure of angle ABC is: 50°.

Learn more about tangent theorem on:

https://brainly.com/question/9892082