Question

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

Explanation:

Step1: Use the triangle angle - sum theorem

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

Step2: Solve for \(x\)

First, simplify the left - hand side of the equation: \(x+(35 + 102)^{\circ}=180^{\circ}\), which is \(x + 137^{\circ}=180^{\circ}\). Then, subtract \(137^{\circ}\) from both sides: \(x=180^{\circ}-137^{\circ}\).

Answer:

\(43\)