Question

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

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 formula is \(\angle JKL=\frac{1}{2}(m\overset{\frown}{JML}-m\overset{\frown}{JL})\). The measure of a full - circle arc is \(360^{\circ}\), so \(m\overset{\frown}{JML} = 360^{\circ}-m\overset{\frown}{JL}\). Given \(m\overset{\frown}{JL}=60^{\circ}\), then \(m\overset{\frown}{JML}=360^{\circ}- 60^{\circ}=300^{\circ}\).

Step2: Calculate the measure of \(\angle JKL\)

Substitute \(m\overset{\frown}{JML} = 300^{\circ}\) and \(m\overset{\frown}{JL}=60^{\circ}\) into the formula \(\angle JKL=\frac{1}{2}(m\overset{\frown}{JML}-m\overset{\frown}{JL})\).

$$
LATEXBLOCK0
$$

Answer:

\(120^{\circ}\)