Question

list the angle measures of δxyz in order from smallest to largest. assume that u is a positive number.
x
27u
98°
y
96u
z
m∠ < m∠ < m∠
submit

Explanation:

Step1: Relate sides to opposite angles

In $\triangle XYZ$:

• Side $XY=27u$ is opposite $\angle Z$
• Side $YZ=96u$ is opposite $\angle X$
• Side $XZ$ is opposite $\angle Y$ (given $m\angle Y=98^\circ$)

Step2: Compare side lengths

Since $u>0$, $27u < 96u$. By the triangle side-angle relationship, the smaller side corresponds to the smaller opposite angle, so $m\angle Z < m\angle X$.

Step3: Confirm largest angle

$\angle Y$ is $98^\circ$, which is greater than $90^\circ$, so it is the largest angle (the sum of the other two angles is $180^\circ-98^\circ=82^\circ$, so both are less than $98^\circ$).

Answer:

$m\angle Z < m\angle X < m\angle Y$