High School

If angle \( KLM \) and \( MLN \) are complementary, and ray \( LM \) bisects angle \( KLN \), find the measures of angle \( KLM \) and angle \( MLN \).

Answer :

Final answer:

Angle KLM and angle MLN are both 45 degrees.

Explanation:

Given that angles KLM and MLN are complementary and that ray LM bisects angle KLN, we can find the measures of angle KLM and angle MLN.

We know that complementary angles add up to 90 degrees, so KLM + MLN = 90. Since ray LM bisects angle KLN, it divides it into two equal angles. This means that KLM and MLN are equal.

So, KLM = MLN = 90/2 = 45 degrees.

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