Question

in $\triangle xyz$, $yz = 11$, $zx = 10$, and $xy = 19$. which statement about the angles of $\triangle xyz$ must be true?

answer

$\circ$ $m\angle x < m\angle z < m\angle y$ $\circ$ $m\angle y < m\angle z < m\angle x$
$\circ$ $m\angle y < m\angle x < m\angle z$ $\circ$ $m\angle z < m\angle y < m\angle x$
$\circ$ $m\angle z < m\angle x < m\angle y$ $\circ$ $m\angle x < m\angle y < m\angle z$

Explanation:

Step1: Match sides to opposite angles

In $\triangle XYZ$:

• Side opposite $\angle X$: $YZ = 11$
• Side opposite $\angle Y$: $ZX = 10$
• Side opposite $\angle Z$: $XY = 19$

Step2: Order sides by length

$10 < 11 < 19$, so $ZX < YZ < XY$

Step3: Relate to angle measures

In a triangle, the larger side corresponds to the larger opposite angle. So:
$m\angle Y < m\angle X < m\angle Z$

Answer:

$\boldsymbol{m\angle Y < m\angle X < m\angle Z}$