Question

a side of the triangle below has been extended to form an exterior angle of 163°. find the value of x.

Explanation:

Step1: Find the adjacent interior angle

The adjacent interior angle and the exterior angle of \(163^{\circ}\) are supplementary. So the adjacent interior angle is \(180 - 163=17^{\circ}\).

Step2: Use the triangle angle - sum property

The sum of angles in a triangle is \(180^{\circ}\). Let the three angles of the triangle be \(17^{\circ}\), \(115^{\circ}\), and \(x^{\circ}\). Then \(x + 17+115 = 180\).
Simplify the left - hand side: \(x+132 = 180\).
Subtract 132 from both sides: \(x=180 - 132\).

Answer:

\(x = 48\)