Question

1. list the side lengths from shortest to longest for each diagram.

a.
l
28°
m
118°
k
-
m
b.
w
64°
x
27°
a
c
67°
y
79°
d
z

Explanation:

Step1: Recall angle - side relationship in a triangle

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

Step2: Find angles and corresponding sides for triangle LKM

First, find the third angle of $\triangle LKM$. Let the third angle be $\angle M$. Using the angle - sum property of a triangle ($\angle L+\angle K+\angle M = 180^{\circ}$), we have $\angle M=180^{\circ}-(118^{\circ} + 28^{\circ})=34^{\circ}$. The angles in ascending order are $\angle L = 28^{\circ},\angle M=34^{\circ},\angle K = 118^{\circ}$. The sides opposite these angles are $k,m,l$ respectively. So the order of side - lengths from shortest to longest is $k,m,l$.

Step3: Find angles and corresponding sides for triangle WXY

First, find the third angle of $\triangle WXY$. Let the third angle be $\angle W$. Using the angle - sum property of a triangle ($\angle W+\angle X+\angle Y=180^{\circ}$), we have $\angle W = 180^{\circ}-(27^{\circ}+67^{\circ}) = 86^{\circ}$. The angles in ascending order are $\angle X = 27^{\circ},\angle Y=67^{\circ},\angle W = 86^{\circ}$. The sides opposite these angles are $w,y,x$ respectively. So the order of side - lengths from shortest to longest is $w,y,x$.

Answer:

a. $k,m,l$
b. $w,y,x$