Question

point m lies in the interior of \\( \angle j k l \\).
use the angle addition postulate to complete the conclusion.

move a choice into the space provided.

\\( m \angle j k l \\)
\\( + \mathrm { m } \angle m k l = \mathrm { m } \angle j k m \\)
\\( = \mathrm { m } \angle m k l + \mathrm { m } \angle m k l \\)
\\( = \mathrm { m } \angle j k m + \mathrm { m } \angle m k l \\)
\\( + \mathrm { m } \angle j k m = \mathrm { m } \angle m k l \\)

Explanation:

Step1: Recall the Angle Addition Postulate

The Angle Addition Postulate states that if a point lies in the interior of an angle, the measure of the larger angle is equal to the sum of the measures of the two smaller angles formed.

Step2: Apply the postulate to \(\angle JKL\)

Since \(M\) is in the interior of \(\angle JKL\), \(\angle JKL\) is composed of \(\angle JKM\) and \(\angle MKL\). So, \(m\angle JKL=m\angle JKM + m\angle MKL\)

Answer:

\(m\angle JKL=m\angle JKM + m\angle MKL\) (the third option)