Question

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

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(75 + 42 + (8x + 15)=180\).

Step2: Simplify the left - hand side

First, add the constant terms: \(75+42 + 15=132\). The equation becomes \(132+8x = 180\).

Step3: Solve for x

Subtract 132 from both sides: \(8x=180 - 132=48\). Then divide both sides by 8: \(x=\frac{48}{8}=6\).

Answer:

\(x = 6\)