Question

the circle below has center m. suppose that m kl = 122°. find the following. (a) m∠kml = (b) m∠kjl =

Explanation:

Step1: Recall central - angle theorem

The measure of a central angle is equal to the measure of its intercepted arc. Here, $\angle KML$ is a central angle and $\overparen{KL}$ is the intercepted arc.

Step2: Find $m\angle KML$

Since $m\overparen{KL}=122^{\circ}$, then $m\angle KML = 122^{\circ}$ (by the central - angle theorem).

Step3: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. $\angle KJL$ is an inscribed angle and $\overparen{KL}$ is its intercepted arc.

Step4: Calculate $m\angle KJL$

We know that $m\angle KJL=\frac{1}{2}m\overparen{KL}$. Substituting $m\overparen{KL} = 122^{\circ}$, we get $m\angle KJL=\frac{1}{2}\times122^{\circ}=61^{\circ}$.

Answer:

(a) $m\angle KML = 122^{\circ}$
(b) $m\angle KJL = 61^{\circ}$