Question

a side of the triangle below has been extended to form an exterior angle of 117°. find the value of x.

Explanation:

Step1: Recall exterior - angle property

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let the non - adjacent interior angles to the given exterior angle be \(x\) and another angle (assume the other non - adjacent interior angle is \(y\)). Here we assume the other non - adjacent interior angle is \(0^{\circ}\) (since no other angle information is given and we consider the basic case where the exterior angle is related to a single non - adjacent interior angle). So \(x + 0^{\circ}=117^{\circ}\).

Step2: Solve for \(x\)

Since \(x+0 = 117^{\circ}\), then \(x = 117^{\circ}\).

Answer:

\(117^{\circ}\)