Question

the side lengths of triangle abc are written in terms of the variable p, where p = 3. which is correct regarding the angles of the triangle? m∠a>m∠c>m∠b m∠b>m∠a>m∠c m∠c>m∠a>m∠b m∠c>m∠b>m∠a

Explanation:

Step1: Calculate side - lengths

Given \(p = 3\).
Side \(AB=4p - 1=4\times3-1=11\).
Side \(BC = 3p=3\times3 = 9\).
Side \(AC=p + 4=3 + 4=7\).

Step2: Recall angle - side relationship

In a triangle, the larger the side length, the larger the measure of the opposite angle.
The order of side - lengths from largest to smallest is \(AB>BC>AC\).
The angle opposite \(AB\) is \(\angle C\), the angle opposite \(BC\) is \(\angle A\), and the angle opposite \(AC\) is \(\angle B\).
So the order of angle measures from largest to smallest is \(m\angle C>m\angle A>m\angle B\).

Answer:

C. \(m\angle C>m\angle A>m\angle B\)