Question

the measure of minor arc jl is 60°. what is the measure of angle jkl? 110° 120° 130° 140°

Explanation:

Step1: Recall the property of the 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 sum of the measure of the minor arc \(JL\) and the major arc \(JL\) is \(360^{\circ}\). Let the measure of the minor arc \(JL = 60^{\circ}\), then the measure of the major arc \(JL=360^{\circ}- 60^{\circ}=300^{\circ}\).
The formula for the measure of \(\angle JKL\) (angle formed by two tangents) is \(\angle JKL=\frac{1}{2}(m\overset{\frown}{JL_{\text{major}}}-m\overset{\frown}{JL_{\text{minor}}})\)

Step2: Substitute the values into the formula

Substitute \(m\overset{\frown}{JL_{\text{major}}}=300^{\circ}\) and \(m\overset{\frown}{JL_{\text{minor}}}=60^{\circ}\) into the formula \(\angle JKL=\frac{1}{2}(300 - 60)\)

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Answer:

\(120^{\circ}\) (the second option)