Question

In the diagram of circle O, what is the measure of abc? 34° 45° 68° 73°

Answer 1

Answer: 34

Step-by-step explanation:

Answer 2

Answer:

A. $m\angle ABC=34^{\circ}$

Step-by-step explanation:

We have been given a diagram. We are asked to find the measure of angle ABC.

First of all, we will find measure of major arc AC by subtracting 146 from 360 degrees.

$\text{Measure of arc AC}=360^{\circ}-146^{\circ}$

$\text{Measure of arc AC}=214^{\circ}$

Now, we will use tangent-tangent angle theorem to solve for ABC.

Tangent-Tangent angle theorem states that angle formed by two tangents outside a circle is half the difference of intercepted arcs.

$m\angle ABC=\frac{214^{\circ}-146^{\circ}}{2}$

$m\angle ABC=\frac{68^{\circ}}{2}$

$m\angle ABC=34^{\circ}$

Therefore, the measure of angle ABC is 34 degrees and option A is the correct choice.