Question

list the angle measures of $\triangle hij$ in order from smallest to largest. assume that $z$ is a positive number.
$m\angle\square < m\angle\square < m\angle\square$
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Explanation:

Step1: Identify side lengths

Sides of $\triangle HIJ$: $IJ=8z$, $JH=26z$, $HI$ (unknown, but we use the Triangle Angle-Side Relationship: In a triangle, the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side).

Step2: Match angles to opposite sides

• $\angle H$ is opposite side $IJ=8z$ (shortest side)
• $\angle I$ is opposite side $JH=26z$ (longest side)
• $\angle J$ is given as $99^\circ$, opposite side $HI$ (middle-length side)

Step3: Order angles by side length

Since $8z < HI < 26z$ (as $z>0$), the angles follow: $\angle H < \angle J < \angle I$

Answer:

$m\angle H < m\angle J < m\angle I$