Question

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

Explanation:

Step1: Match sides to opposite angles

• Side $27a$ (EF) ↔ $\angle G$
• Side $35a$ (FG) ↔ $\angle E$
• Side $37a$ (GE) ↔ $\angle F$

Step2: Order sides by length

Since $a>0$, $27a < 35a < 37a$

Step3: Apply triangle angle-side relationship

In a triangle, 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:

$m\angle G < m\angle E < m\angle F$