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

We are given with
arc AC = 130
The measure of the arc on the other side of the circle is
360 - 130 = 230
Therefore, according to the theorem on circles, the measure of angle ABC is 
(1/2) ( 230 - 130) = 50

Answer 2

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= $50$°