Question

a side of the triangle below has been extended to form an exterior angle of 71°. find the value of x.

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, the exterior angle is \(71^{\circ}\), one non - adjacent interior angle is \(49^{\circ}\), and the other non - adjacent interior angle is \(x\). So, \(x + 49^{\circ}=71^{\circ}\).

Step2: Solve for \(x\)

Subtract \(49^{\circ}\) from both sides of the equation \(x + 49^{\circ}=71^{\circ}\). We get \(x=71^{\circ}-49^{\circ}\).

Answer:

\(x = 22\)