Question

in triangle klm, kl < lm < km. which of the following correctly orders the angles from smallest to largest? a) ∠m < ∠k < ∠l b) ∠k < ∠l < ∠m c) ∠l < ∠m < ∠k d) ∠m < ∠l < ∠k your answer consider a triangle where one angle is obtuse (greater than 90°). which side of the triangle must be the longest? a) the side opposite the smallest angle. b) the side opposite the right angle (if one exists) c) the side opposite the obtuse angle. d) any of the sides could be the longest.

Explanation:

Step1: Recall angle - side relationship

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

Step2: Analyze first question

Given $KL

Step3: Analyze second question

In a triangle with an obtuse - angle, the obtuse angle is the largest angle. The side opposite the largest angle is the longest side. So the side opposite the obtuse angle is the longest side.

Answer:

1. a) $\angle M<\angle K<\angle L$
2. c) The side opposite the obtuse angle