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Answer :
By definition, the measures of two complementary angles adds up to 90 degrees. Therefore, the measure of angle KLN is 90 degrees. Because LM bisects KLN, by definition, LM divides KLN in half. Therefore KLM and MLN each measure 45 degrees.
When in doubt, draw a picture.
When in doubt, draw a picture.
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Final answer:
Using the concepts of complementary angles and bisecting angles, we find that Angle KLM measures 60 degrees and Angle MLN measures 30 degrees.
Explanation:
In this problem, we're dealing with complementary angles and bisecting an angle. Complementary angles are two angles whose measures sum to 90 degrees. When an angle is bisected, it is split into two equal smaller angles.
Firstly, as angle KLM and angle MLN are complementary, the sum of their measures equals 90 degrees, so Angle KLM + Angle MLN = 90 degrees.
Secondly, as angle LM is bisecting angle KLM, this means that angle KLM is split into two equal parts. Let's assume each of those parts is x, that means Angle KLM = 2x.
Given that angle KLM and angle MLN are complementary, we can substitute angle KLM = 2x into the equation, leading us to 2x + Angle MLN = 90 degrees. Since angle MLN is also x because it's a part of bisected angle KLM, we can substitute in Angel MLN = x into this equation, ending up with 2x + x = 90 degrees or 3x = 90 degrees. Solving for x, we find that x = 90 / 3 = 30 degrees.
Therefore, the measure of Angle KLM (2x) is 60 degrees and the measure of Angle MLN (x) is 30 degrees.
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