Question

list the side lengths of δefg in order from shortest to longest.

Explanation:

Step1: Sum angles to 180°

$$14b + (b+57) + (b+59) = 180$$

Step2: Simplify and solve for b

$$16b + 116 = 180$$
$$16b = 64$$
$$b = 4$$

Step3: Calculate each angle

• $\angle G = 14(4) = 56^\circ$
• $\angle E = 4+57 = 61^\circ$
• $\angle F = 4+59 = 63^\circ$

Step4: Match sides to opposite angles

Side opposite $\angle G$: $EF$
Side opposite $\angle E$: $FG$
Side opposite $\angle F$: $GE$
Smallest angle → shortest side, largest angle → longest side.

Answer:

$EF < FG < GE$