Question

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

Explanation:

Step1: Recall the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(x + 102+35=180\).

Step2: Simplify the left - hand side of the equation

\(x+(102 + 35)=x + 137\). The equation becomes \(x+137 = 180\).

Step3: Solve for \(x\)

Subtract 137 from both sides of the equation: \(x=180 - 137\).

Answer:

\(x = 43\)