Question

80° (2x)° 140°

Explanation:

Step1: Find the adjacent interior angle

The sum of an interior angle and its adjacent exterior angle is \(180^{\circ}\). Let the adjacent interior angle be \(y\). Then \(y + 140^{\circ}=180^{\circ}\), so \(y = 180^{\circ}- 140^{\circ}=40^{\circ}\).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). In the triangle, we have \(80^{\circ}+2x + y=180^{\circ}\). Substitute \(y = 40^{\circ}\) into the equation: \(80^{\circ}+2x+40^{\circ}=180^{\circ}\).
First, simplify the left - hand side: \(2x+120^{\circ}=180^{\circ}\).
Then, subtract \(120^{\circ}\) from both sides: \(2x=180^{\circ}-120^{\circ}\), so \(2x = 60^{\circ}\).
Finally, divide both sides by 2: \(x=\frac{60^{\circ}}{2}=30^{\circ}\).

Answer:

\(x = 30\)