Question

which list orders the angles of triangle abc from smallest to largest measure?

a. ∠a, ∠c, ∠b
b. ∠c, ∠a, ∠b
c. ∠b, ∠c, ∠a
d. ∠a, ∠b, ∠c

Explanation:

Step1: Recall the triangle - side - angle relationship

In a triangle, the larger the side length, the larger the angle opposite it.

Step2: Identify the sides and their opposite angles

In \(\triangle ABC\), side \(BC = 180\) (opposite \(\angle A\)), side \(AC=120\) (opposite \(\angle B\)), side \(AB = 130\) (opposite \(\angle C\)).
Since \(AC

Step3: Order the angles

The angle opposite \(AC\) is \(\angle B\), the angle opposite \(AB\) is \(\angle C\), and the angle opposite \(BC\) is \(\angle A\). So, \(\angle B<\angle C<\angle A\)

Answer:

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