Question

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

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180°. So, we set up the equation \(75+(8x + 15)+42=180\).

Step2: Combine like - terms

\(75+15 + 42+8x=180\), which simplifies to \(132+8x=180\).

Step3: Isolate the variable term

Subtract 132 from both sides: \(8x=180 - 132\), so \(8x=48\).

Step4: Solve for x

Divide both sides by 8: \(x=\frac{48}{8}\).

Answer:

\(x = 6\)