Question

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

Explanation:

Step1: Sum angles to 180°

$$(p-5^\circ)+(p+18^\circ)+(p+8^\circ)=180^\circ$$

Step2: Simplify to solve for p

$$3p + 21^\circ=180^\circ \implies 3p=159^\circ \implies p=53^\circ$$

Step3: Calculate each angle

• $\angle G = 53^\circ - 5^\circ = 48^\circ$
• $\angle E = 53^\circ + 18^\circ = 71^\circ$
• $\angle F = 53^\circ + 8^\circ = 61^\circ$

Step4: Match sides to opposite angles

Side opposite $\angle G$: $EF$
Side opposite $\angle F$: $EG$
Side opposite $\angle E$: $FG$
Order angles: $48^\circ < 61^\circ < 71^\circ$

Answer:

$EF < EG < FG$