Question

list the angle measures of \\(\triangle cde\\) in order from smallest to largest. assume that \\(u\\) is a positive number.
\\(m\angle\square < m\angle\square < m\angle\square\\)

Explanation:

Step1: Pair angles with opposite sides

In $\triangle CDE$:

• $\angle C$ is opposite side $DE = 30u$
• $\angle D$ is opposite side $CE = 40u$
• $\angle E$ is opposite side $CD = 45u$

Step2: Compare side lengths

Since $u>0$, $30u < 40u < 45u$

Step3: Apply triangle angle-side theorem

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

Answer:

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