Question

the lengths of the sides of triangle abc are represented in terms of the variable m, where m > 6. ab = m - 2 bc = m + 4 ac = m list the angles from smallest to largest. angle, angle, angle

Explanation:

Step1: Compare side lengths

We have \( AB = m - 2 \), \( BC = m + 4 \), \( AC = m \), and \( m>6 \).
To compare \( AB \) and \( AC \): \( m-(m - 2)=2>0 \), so \( AC>AB \) (since \( m-(m - 2)=m - m + 2 = 2>0 \)).
To compare \( AC \) and \( BC \): \( (m + 4)-m = 4>0 \), so \( BC>AC \).
So the order of side lengths from shortest to longest is \( AB

Step2: Relate sides to angles

In a triangle, the larger the side length, the larger the opposite angle.
The angle opposite \( AB \) is \( \angle C \), the angle opposite \( AC \) is \( \angle B \), and the angle opposite \( BC \) is \( \angle A \).
Since \( AB

Answer:

\(\angle C\), \(\angle B\), \(\angle A\)