Question

jk is tangent to the circle at l. find the measure of ∠jlm. 282° write your answer as a whole number or a decimal. m∠jlm = °

Explanation:

Step1: Recall the tangent - arc relationship

The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.

Step2: Find the measure of the intercepted arc

The whole circle is 360°. The given arc is 282°, so the intercepted arc for ∠JLM is \(360 - 282= 78^{\circ}\).

Step3: Calculate the measure of ∠JLM

By the tangent - chord angle formula, \(m\angle JLM=\frac{1}{2}\times\) (measure of the intercepted arc). So \(m\angle JLM=\frac{1}{2}\times78 = 39^{\circ}\).

Answer:

39