Question

the measures of the angles of a triangle are shown in the figure below. solve for x.

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(80^{\circ}+38^{\circ}+(5x + 12)^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

First, combine the constant terms: \(80 + 38+12+5x=180\). Since \(80+38 + 12=130\), the equation becomes \(130+5x=180\).

Step3: Solve for \(x\)

Subtract \(130\) from both sides of the equation: \(5x=180 - 130\). So, \(5x=50\). Then divide both sides by \(5\): \(x=\frac{50}{5}\).

Answer:

\(x = 10\)