Question

a side of the triangle below has been extended to form an exterior angle of 121°. find the value of x.

Explanation:

Step1: Recall the exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In a right - angled triangle, one of the non - adjacent interior angles is \(90^{\circ}\), and the exterior angle is \(121^{\circ}\). Let the other non - adjacent interior angle be \(x\). Then, according to the exterior angle theorem, \(x + 90^{\circ}=121^{\circ}\).

Step2: Solve for \(x\)

Subtract \(90^{\circ}\) from both sides of the equation \(x + 90^{\circ}=121^{\circ}\). So, \(x=121^{\circ}-90^{\circ}\).

Answer:

\(x = 31^{\circ}\)