Question

In the diagram of circle O, what is the measure of ? 27° 54° 108° 120°

Answer 1

Answer:

Option (2).

Step-by-step explanation:

This question is incomplete; here is the complete question and find the figure attached.

In the diagram of a circle O, what is the measure of ∠ABC?

27°

54°

108°

120°

m(minor arc $\widehat {AC}$) = 126°

m(major arc $\widehat {AC}$) = 234°

By the intersecting tangents theorem,

If the two tangents of a circle intersect each other outside the circle, measure of angle formed between them is half the difference of the measures of the intercepted arcs.

m∠ABC = $\frac{1}{2}[m(\text {major arc{AC})}-m(\text{minor arc} {AC})]$

             = $\frac{1}{2}(234-126)$

             = 54°

Therefore, Option (2) will be the answer.

Answer 2

Answer:

B.

Step-by-step explanation: