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 have the equation \(75+(8x + 15)+42=180\).

Step2: Combine like - terms

First, add the constant terms on the left - hand side: \(75 + 15+42+8x=180\), which simplifies to \(132 + 8x=180\).

Step3: Isolate the variable term

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

Step4: Solve for x

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

Answer:

\(x = 6\)