Question

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

Explanation:

Step1: Recall the sum of angles in a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\).

Step2: Set up the equation

Let the right - angle be \(90^{\circ}\), one angle be \(50^{\circ}\), and the other angle be \(x\). Then \(x + 50^{\circ}+90^{\circ}=180^{\circ}\).

Step3: Solve the equation for \(x\)

Simplify the left - hand side: \(x+140^{\circ}=180^{\circ}\).
Subtract \(140^{\circ}\) from both sides: \(x = 180^{\circ}-140^{\circ}\).

Answer:

\(x = 40^{\circ}\)