Question

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

Explanation:

Step1: Find ∠HJ K

Since ∠IJ H and ∠HJ K are supplementary (they form a linear pair), we have:
$\angle HJK = 180^\circ - 142^\circ = 38^\circ$

Step2: Find ∠H

In $\triangle HJK$, the sum of interior angles is $180^\circ$. We know $\angle K = 67^\circ$ and $\angle HJK = 38^\circ$, so:
$\angle H = 180^\circ - 67^\circ - 38^\circ = 75^\circ$

Step3: Order angles from smallest to largest

The angles of $\triangle HJK$ are: $\angle HJK = 38^\circ$, $\angle K = 67^\circ$, $\angle H = 75^\circ$. So the order from smallest to largest is $\angle HJK < \angle K < \angle H$.

Step4: Relate angles to sides (larger angle opposite longer side)

In a triangle, the longer side is opposite the larger angle. So:

• Side opposite $\angle HJK$ (38°) is $HK$
• Side opposite $\angle K$ (67°) is $HJ$
• Side opposite $\angle H$ (75°) is $JK$

Thus, the order of sides from shortest to longest is $HK < HJ < JK$.

Answer:

$HK$, $HJ$, $JK$