Question

list the angle measures of δhij in order from smallest to largest, given that hj = 25 miles, ij = 37 miles, and hi = 23 miles. m∠□ < m∠□ < m∠□

Explanation:

Step1: Match sides to opposite angles

In $\triangle HIJ$:

• Side $HI=23$ is opposite $\angle J$
• Side $HJ=25$ is opposite $\angle I$
• Side $IJ=37$ is opposite $\angle H$

Step2: Order sides by length

$23 < 25 < 37$, so $HI < HJ < IJ$

Step3: Relate to angle measures

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

Answer:

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