We want to find m∠JMK. We know that if two secants or chords intersect inside the circle, then the measure of an angle formed is half the sum of the arcs intercepted by the angle and its vertical angle.
m∠KML = 1/2(mHJ+ mLK)
Let's substitute the known values and simplify.
Note that ∠JML is a straight angle, which measures 180^(∘). By the Segment Addition Postulate, we can write the following equation.
m ∠JMK + m ∠KML = 180
↓
m∠JMK + 78 = 180
Finally, let's solve it for m∠JMK.
