Question

list the side lengths of $\triangle fgh$ in order from shortest to longest.

Explanation:

Step1: Find ∠GHI's supplement

The angle ∠GHI is 135°, so its supplementary angle (∠FHG) inside △FGH is:
$180^\circ - 135^\circ = 45^\circ$

Step2: Calculate ∠F

Use triangle angle sum ($180^\circ$):
$\angle F = 180^\circ - 63^\circ - 45^\circ = 72^\circ$

Step3: Match sides to opposite angles

In a triangle, the shortest side is opposite the smallest angle, and the longest side is opposite the largest angle:

• Smallest angle: $45^\circ$ (opposite $\overline{FG}$)
• Middle angle: $63^\circ$ (opposite $\overline{FH}$)
• Largest angle: $72^\circ$ (opposite $\overline{GH}$)

Answer:

$\overline{FG} < \overline{FH} < \overline{GH}$