Question

billiards a billiards ball rack can be modeled by △abc. solve for x.

Explanation:

Step1: Identify triangle type

The billiards rack is an equilateral triangle, so all angles are \(60^\circ\). Thus, \(\angle C = 60^\circ\).

Step2: Set up equation

Given \(\angle C=(3x - 6)^\circ\), set \(3x-6 = 60\).

Step3: Solve for x

Add 6 to both sides: \(3x=60 + 6=66\).
Divide by 3: \(x=\frac{66}{3}=22\).

Answer:

\(x = 22\)