Question

list the angle measures of $\triangle cde$ in order from smallest to largest. assume that $u$ is a positive number.

(image of triangle $cde$ with side $cd$ labeled $45u$, side $ce$ labeled $48u$, side $de$ labeled $31u$)

Explanation:

Step1: Match angles to opposite sides

In $\triangle CDE$:

• $\angle C$ is opposite side $DE = 31u$
• $\angle D$ is opposite side $CE = 48u$
• $\angle E$ is opposite side $CD = 45u$

Step2: Compare side lengths

Since $u>0$, compare the coefficients:
$31 < 45 < 48$, so $31u < 45u < 48u$

Step3: Relate sides to angles

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

Answer:

$m\angle C < m\angle E < m\angle D$