Question

In AKLM, mZK = 101° and mL = 67º. Which statement about the sides of AKLM

must be true?
LM > MK > KL
LM > KL > MK
O KL > MK > LM
O KL > LM > MK
MK > KL > LM
O MK > LM > KL

Answer 1

LM > MK > KL

Explanation:

Given: ΔKLM , m∠K = 101° , m∠L = 67°

By definition of a triangle's sum of interior angles, the ∑ΔKLM's interior angles is 180°, ∴ m∠M = 180 - (101 + 67) = 12°

By the usage of law of sines, the opposite side's measurement is contingent with the angle measurement. The smaller the angle measurement, the shorter the opposite side.

Note the angles:

m∠M = 12° ∴ Side LK = shortest

m∠K = 101° ∴ Side ML = longest

m∠L = 67° ∴ Side KM = in between

∴ LK < KM < ML

A) LM > MK > KL is your answer.

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