Question

in δklm, m∠k = 21° and m∠l = 36°. which list has the sides of δklm in order from longest to shortest?

answer

○ kl, lm, mk ○ kl, mk, lm
○ mk, lm, kl ○ mk, kl, lm
○ lm, mk, kl ○ lm, kl, mk

Explanation:

Step1: Find measure of ∠M

In a triangle, the sum of angles is \(180^\circ\). So, \(m\angle M = 180^\circ - m\angle K - m\angle L\). Substituting \(m\angle K = 21^\circ\) and \(m\angle L = 36^\circ\), we get \(m\angle M = 180 - 21 - 36 = 123^\circ\).

Step2: Relate angles to side lengths

In a triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. The angles in order from largest to smallest are \( \angle M (123^\circ) \), \( \angle L (36^\circ) \), \( \angle K (21^\circ) \). So the sides opposite these angles (opposite \( \angle M \) is \( KL \), opposite \( \angle L \) is \( MK \), opposite \( \angle K \) is \( LM \)) will be in order from longest to shortest as \( KL \) (opposite \(123^\circ\)), \( MK \) (opposite \(36^\circ\)), \( LM \) (opposite \(21^\circ\)).

Answer:

KL, MK, LM