Question

list the angle measures of $\triangle abc$ in order from smallest to largest. assume that $w$ is a positive number.
$m\angle\square < m\angle\quad < m\angle\quad$

Explanation:

Step1: Match sides to opposite angles

• Side $30w$ (BC) ↔ $\angle A$
• Side $49w$ (AB) ↔ $\angle C$
• Side $51w$ (AC) ↔ $\angle B$

Step2: Order side lengths

$30w < 49w < 51w$

Step3: Apply triangle angle-side theorem

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

Answer:

$m\angle A < m\angle C < m\angle B$