Question

in △xyz, m∠x = 42° and m∠y = 127°. which statement about the sides of △xyz must be true? answer
○ zx < yz < xy
○ yz < xy < zx
○ zx < xy < yz
○ yz < zx < xy
○ xy < zx < yz
○ xy < yz < zx

Explanation:

Step1: Find angle Z

The sum of angles in a triangle is 180°. So, $m\angle Z=180^{\circ}-m\angle X - m\angle Y=180^{\circ}-42^{\circ}-127^{\circ}=11^{\circ}$.

Step2: Recall angle - side relationship

In a triangle, the side opposite the smallest angle is the shortest and the side opposite the largest angle is the longest. Here, $\angle Z < \angle X<\angle Y$. The side opposite $\angle Z$ is $XY$, the side opposite $\angle X$ is $YZ$, and the side opposite $\angle Y$ is $ZX$.

Answer:

$XY < YZ < ZX$