Question

list the angle measures of $\triangle ijk$ in order from smallest to largest. assume a is a positive number.
$m\angle\square < m\angle\square < m\angle\square$

Explanation:

Step1: Match angles to opposite sides

In a triangle, each angle is opposite a side:

• $\angle I$ is opposite $JK = 18a$
• $\angle K$ is opposite $JI = 22a$
• $\angle J$ is opposite $KI = 24a$

Step2: Compare side lengths

Since $a>0$, order sides:
$18a < 22a < 24a$

Step3: Relate to angle measures

By the triangle inequality theorem, the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side. So the angles follow the same order as their opposite sides.

Answer:

$m\angle I < m\angle K < m\angle J$