Question

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

Answer 1

B.

Explanation:

Answer 2

Option (2).

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 =
`(1)/(2)[m(\text {major arc{AC})}-m(\text{minor arc} {AC})]`

=
`(1)/(2)(234-126)`

= 54°

Therefore, Option (2) will be the answer.