Question

triangle klm is shown below.
image of triangle klm with angle at m being 62° and angle at l being 58°
which list orders the sides of the triangle from shortest to longest?
○ $overline{mk}$, $overline{ml}$, $overline{kl}$
○ $overline{mk}$, $overline{kl}$, $overline{ml}$
○ $overline{ml}$, $overline{mk}$, $overline{kl}$
○ $overline{kl}$, $overline{ml}$, $overline{mk}$

Explanation:

Step1: Calculate ∠K

Sum of angles in triangle is $180^\circ$.
$\angle K = 180^\circ - 62^\circ - 58^\circ = 60^\circ$

Step2: Match sides to opposite angles

In a triangle, shorter side ↔ smaller opposite angle:

• $\overline{KL}$ opposite $\angle M=62^\circ$
• $\overline{MK}$ opposite $\angle L=58^\circ$
• $\overline{ML}$ opposite $\angle K=60^\circ$

Step3: Order sides by angle size

Sort angles: $58^\circ < 60^\circ < 62^\circ$, so sides: $\overline{MK} < \overline{ML} < \overline{KL}$

Answer:

$\overline{MK}, \overline{ML}, \overline{KL}$