To find the measure of angle JKL given that the measure of minor arc JL is 60 degrees, we can use the relationship between the angle formed at the center of the circle and the arcs it subtends. In a circle, the measure of an angle formed by two radii (central angle) is equal to the measure of the arc it subtends.
However, angle JKL is an inscribed angle that subtends the same arc JL. The inscribed angle is always half the measure of the arc it intercepts. Therefore, we can calculate the measure of angle JKL as follows:
Measure of angle JKL = 1/2 × Measure of arc JL
Substituting the known values:
Measure of angle JKL = 1/2 × 60 degrees = 30 degrees
So, the measure of angle JKL is 30 degrees. This relationship is fundamental in circle geometry and helps us understand how angles and arcs interact within circles.