Question

question in △abc, m∠a = 112° and m∠b = 14°. which statement about the sides of △abc must be true? answer ○ bc < ab < ca ○ ab < ca < bc ○ ca < bc < ab ○ ca < ab < bc ○ ab < bc < ca ○ bc < ca < ab submit answer watch video show examples

Explanation:

Step1: Find the measure of angle \(C\)

The sum of angles in a triangle is \(180^{\circ}\). Given \(m\angle A = 112^{\circ}\) and \(m\angle B=14^{\circ}\), then \(m\angle C=180^{\circ}-(m\angle A + m\angle B)=180^{\circ}-(112^{\circ}+14^{\circ}) = 54^{\circ}\).

Step2: Use the angle - side relationship

In a triangle, the larger the angle, the longer the side opposite it. Since \(m\angle B=14^{\circ}\lt m\angle C = 54^{\circ}\lt m\angle A=112^{\circ}\), the sides opposite these angles follow the same order. The side opposite \(\angle A\) is \(BC\), the side opposite \(\angle B\) is \(AC\), and the side opposite \(\angle C\) is \(AB\). So \(AC\lt AB\lt BC\).

Answer:

\(AC\lt AB\lt BC\)