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, \(75^\circ + 49^\circ + (8x + 15)^\circ = 180^\circ\).

Step2: Simplify left - hand side

First, calculate \(75 + 49+15\): \(75 + 49 = 124\), \(124+15 = 139\). So the equation becomes \(139 + 8x=180\).

Step3: Solve for x

Subtract 139 from both sides: \(8x = 180 - 139\), \(8x = 41\). Then divide both sides by 8: \(x=\frac{41}{8}=5.125\).

Answer:

\(x = 5.125\)