Answer:
m < LKH = 69°
Step-by-step explanation:
Given that m < LKM = 111° and that:
<LKM and <LKH are adjacent angles as they share the same vertex, point K, and same ray between them, KL:
Then we can assume that m < LKM and m < LKH are supplementary angles whose sum = 180°.
Therefore, we can establish the following equation:
m < LKM + m < LKH = 180°
111° + m <LKH = 180°
Subtract 111° from both sides to solve for m < LKH:
111° - 111° + m <LKH = 180° - 111°
m < LKH = 69°
Therefore, the measure of < LKH is 69°.
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