Question

1. given ( x = 5 ), which angle is the smallest, ( angle a, angle b ), or ( angle c )?

Explanation:

Step1: Substitute \(x = 5\) into the expressions for the sides

• For side \(CA\): \(2x-4\). Substitute \(x = 5\), we get \(2\times5 - 4=10 - 4 = 6\).
• For side \(AB\): \(x\). Substitute \(x = 5\), we get \(x=5\).
• For side \(CB\): \(3x - 11\). Substitute \(x = 5\), we get \(3\times5-11=15 - 11 = 4\).

Step2: Recall the triangle - angle relationship

In a triangle, the smallest angle is opposite the shortest side.

Since \(CB = 4\), \(AB = 5\), \(CA=6\), and \(CB\) is the shortest side.

The angle opposite \(CB\) is \(\angle A\).

Answer:

A.