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 = ° submit

Explanation:

Step1: Find the minor arc measure

The total circle is \(360^\circ\). The major arc \(LM\) is \(282^\circ\), so the minor arc \(LM\) is \(360 - 282 = 78^\circ\).

Step2: Use tangent - chord angle theorem

The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. So \(\angle JLM=\frac{1}{2}\times\) measure of minor arc \(LM\).
Substitute the minor arc measure: \(\angle JLM=\frac{1}{2}\times78 = 39^\circ\).

Answer:

\(39\)