Final answer:
The measure of \(m\angle JKM\) is found by subtracting the measure of \(m\angle MKL\), which is 42 degrees, from the measure of \(m\angle JKL\), which is 84 degrees, resulting in \(m\angle JKM\) being 42 degrees.
Step-by-step explanation:
To find the measure of \(m\angle JKM\), we must recognize that point M lies within \(\angle JKL\), meaning the sum of \(m\angle JKM\) and \(m\angle MKL\) is equal to the measure of \(m\angle JKL\), which is given as 84 degrees.
Since \(m\angle MKL\) is 42 degrees, we can determine \(m\angle JKM\) by subtracting the measure of \(m\angle MKL\) from the measure of \(m\angle JKL\). Therefore, \(m\angle JKM = m\angle JKL - m\angle MKL = 84^\circ - 42^\circ = 42^\circ\).
To find the measure of ∠JKM, we can use the Angle Sum Theorem, which states that the sum of the measures of the angles of a triangle is always 180 degrees.
Since we know that ∠MKL = 42 degrees and ∠JKL = 84 degrees, we can find the measure of ∠JKM by subtracting the sum of these two angles from 180 degrees: ∠JKM = 180 - (42 + 84) = 54 degrees.
Therefore, the measure of ∠JKM is 54 degrees.