We are given a circle with center $M$. The measure of arc $KL$ is given as $m \widehat{KL} = 74^\circ$. We need to find: (a) $m \angle KML$ (b) $m \angle KJL$

1. Problem Description

We are given a circle with center $M$. The measure of arc $KL$ is given as $m \widehat{KL} = 74^\circ$.

We need to find:

(a) $m \angle KML$

(b) $m \angle KJL$

2. Solution Steps

(a) The measure of a central angle is equal to the measure of its intercepted arc. Therefore,

$m \angle KML = m \widehat{KL}$.

Since $m \widehat{KL} = 74^\circ$, we have $m \angle KML = 74^\circ$.

(b) The measure of an inscribed angle is half the measure of its intercepted arc.

$m \angle KJL = \frac{1}{2} m \widehat{KL}$

Since $m \widehat{KL} = 74^\circ$, we have $m \angle KJL = \frac{1}{2} (74^\circ) = 37^\circ$.

3. Final Answer

(a) $m \angle KML = 74^\circ$

(b) $m \angle KJL = 37^\circ$