Question

Question was provided via image upload.

Explanation:

Step1: Find the base angles of the isosceles triangle

Since the triangle is isosceles (two sides are equal), the base angles are equal. Let the base angles be \( y\). Using the angle - sum property of a triangle (\(y + y+62^{\circ}=180^{\circ}\)).

$$2y=180^{\circ}- 62^{\circ}$$

$$2y = 118^{\circ}$$

$$y = 59^{\circ}$$

Step2: Use the exterior - angle relationship

The exterior angle \(x\) is equal to the sum of the two non - adjacent interior angles of the triangle. Here, \(x\) is an exterior angle and the two non - adjacent interior angles are \(62^{\circ}\) and \(59^{\circ}\)

$$x=62^{\circ}+59^{\circ}$$

Answer:

\(x = 121^{\circ}\)