The measure of minor arc JL is 60°. What is the measure of angle JKL?

finding the measure of the arc JKL

Solution:

From the figure, we observe that

JML is the central angle

The measure of angle JML = the measure of arc JL

The measure of angle JML = 60°

The tangent of a circle is perpendicular to the radius

Tangent KJ is a tangent to the circle at point J

Tangent KL is a tangent to the circle at point L

The measure of angle KJM = Measure of angle KLM = 90°

JKLM is a quadrilateral

All the angles of a quadrilateral = 360°

∠JKL + ∠KLM + ∠LMJ + ∠MJK = 360°

Substituting the values

∠JKL + 90° + 60° + 90° = 360°

∠JKL + 240° = 360°

Subtracting both sides by 240°

∠JKL = 360° - 240°

∠JKL = 120°

Therefore, the measure of angle JKL is 120°.

The measure of minor arc JL is 60°. What is the measure of angle JKL?

Summary:

The measure of minor arc JL is 60°. The measure of angle JKL is 120°.

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