Question

In triangle JKL, where angle JKL measures 56.4 degrees and angle JKM measures 82.5 degrees, what is the measure of angle LKM (angle LKM = ?).

A) 61.1 degrees
B) 18.9 degrees
C) 101.1 degrees
D) 124.1 degrees

Answer 1

To find the measure of angle LKM in triangle JKL, we subtract the sum of the given angles, JKL and JKM, from 180 degrees. The correct measure is 71.4 degrees, which is not among the provided options.

Step-by-step explanation:

In triangle JKL, we are given that angle JKL measures 56.4 degrees and angle JKM measures 82.5 degrees. To find the measure of angle LKM, we must recognize that JKL is part of a larger picture involving triangle JKM. The sum of the angles in any triangle is 180 degrees. Therefore, we can find the measure of angle LJK by subtracting angle JKL from angle JKM:

Angle LJK = Angle JKM - Angle JKL = 82.5 degrees - 56.4 degrees = 26.1 degrees.

Now, to find the measure of angle LKM, we look at triangle JKM. In this triangle, once we have two angles, we can find the third by subtracting the sum of the known angles from 180 degrees:

Angle LKM = 180 degrees - Angle JKM - Angle LJK = 180 degrees - 82.5 degrees - 26.1 degrees = 71.4 degrees.

Therefore, none of the provided options A) 61.1 degrees, B) 18.9 degrees, C) 101.1 degrees, or D) 124.1 degrees is correct. The measure of angle LKM is actually 71.4 degrees.