Question

determine the value of \\(x\\) for this equilateral triangle.

\\((16x + 12)^\circ\\)

\\(x = 3\\)
\\(x = 60\\)
\\(x = \frac{9}{2}\\)
\\(x = \frac{2}{3}\\)

Explanation:

Identify properties of the triangle

Using the Equilateral Triangle Properties knowledge point, we know that an equilateral triangle has three equal sides and three equal interior angles. Since the sum of the interior angles of any triangle is \(180^\circ\), each interior angle in an equilateral triangle must measure exactly \(60^\circ\).

Set up the algebraic equation

The image shows one of the interior angles labeled as \((16x + 12)^\circ\). Since each angle of this equilateral triangle is \(60^\circ\), we can set up the following equation:

$$16x + 12 = 60$$

Solve for x

We solve the linear equation step-by-step:
Subtract \(12\) from both sides:

$$16x = 48$$

Divide both sides by \(16\):

$$x = \frac{48}{16}$$

$$x = 3$$

Answer:

• (A) \(x = 3\) (Correct answer)
• (B) \(x = 60\)
• (C) \(x = \frac{9}{2}\)
• (D) \(x = \frac{4}{3}\)