Question

In the diagram below, AB and BC are tangent to O. What is the measure of angle B?
APEX

Answer 1

option C <B = 54° ( answer is attached )

Answer 2

Answer:

C. $54^o$

Step-by-step explanation:

We have been given a circle O. AB and AC are tangent of our given circle.

Since angle B is formed by tangents outside our given circle, so we will use tangent-tangent theorem.

Tangent-Tangent theorem states that when an angle is formed outside the circle by two tangents, then the measure of angle equals half the difference of its corresponding arcs.

$m\angle B=\frac{\text{Major arc - Minor arc}}{2}$

$m\angle B=\frac{234^o-126^o}{2}$

$m\angle B=\frac{108^o}{2}$

$m\angle B=54^o$

Therefore, the measure of angle B is 54 degrees and option C is the correct choice.