Answer problem below

The measure of arc JL is 24degrees

According to the theorem

The angle at the vertex is half that of the intercepted arc. This means that;

Angle JKL = 1/2(128 - arcJL)

Solve for arc JL

From the diagram, we can see that <NJM = 1/2 theta

<NJM = 1/2 * 128

<NJM = 64degrees

Get <MJK

<MJK = 180 - <NJM

<MJK = 180 - 64

<MJK = 116degres

From triangle JKM, hence;

<JMK + <MJK + <JKL = 180

<JMK + 116 + 52 = 180

<JMK + 168 = 180

<JMK = 12degrees

Get arc JL

arcJL = 2(<JMK)

arc JL = 2(12)

arc JL = 24degrees

Hence the measure of arc JL is 24degrees

Learn more on angles here:

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hope this !