Question

80° 50° x° x = 120 x = 130 x = 140 x = 150

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. Let the third - interior angle of the triangle be \(y\). So, \(y+80^{\circ}+50^{\circ}=180^{\circ}\).

Step2: Solve for the third - interior angle \(y\)

\(y = 180^{\circ}-(80^{\circ}+50^{\circ})=180^{\circ}-130^{\circ}=50^{\circ}\).

Step3: Use the linear - pair property

The angle \(x\) and the interior angle \(y\) form a linear pair. A linear pair of angles sums to 180°. So, \(x + y=180^{\circ}\). Since \(y = 50^{\circ}\), then \(x=180^{\circ}-50^{\circ}=130^{\circ}\).

Answer:

\(x = 130\)