Question

in the diagram of circle o, what is the measure of ∠abc? 27° 54° 108° 120°

Explanation:

Step1: Use the formula for the measure of an angle formed by two tangents

The measure of an angle formed by two tangents drawn from an external point to a circle is half the difference of the measures of the intercepted arcs. The formula is \( \angle ABC=\frac{1}{2}(m\overset{\frown}{major\ arc}-m\overset{\frown}{minor\ arc})\)

Step2: Identify the major and minor arcs

Here, the major arc is \(234^{\circ}\) and the minor arc is \(126^{\circ}\)

Step3: Substitute the values into the formula

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Answer:

\(54^{\circ}\) (the second option)