Question

order the angle measures $m\angle a$, $m\angle b$, and $m\angle c$ from least to greatest.
(note that the figure is not drawn to scale.)
triangle with vertices a, b, c; side ac = 12, side ab = 11, side bc = 8
$m\angle \square$ $<$ $m\angle \square$ $<$ $m\angle \square$

Explanation:

Step1: Recall Triangle Angle-Side Relationship

In a triangle, the larger the side opposite an angle, the larger the angle. So we first identify the sides opposite each angle.

• Side opposite \( \angle A \): \( BC = 8 \)
• Side opposite \( \angle B \): \( AC = 12 \)
• Side opposite \( \angle C \): \( AB = 11 \)

Step2: Order the Sides by Length

Order the sides from shortest to longest: \( BC = 8 \) (opposite \( \angle A \)), \( AB = 11 \) (opposite \( \angle C \)), \( AC = 12 \) (opposite \( \angle B \)).

Step3: Order the Angles by Their Opposite Sides

Since the shortest side is opposite the smallest angle, and the longest side is opposite the largest angle, we have: \( m\angle A < m\angle C < m\angle B \).

Answer:

\( m\angle A < m\angle C < m\angle B \)