Question

a side of the triangle below has been extended to form an exterior angle of 157°. 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 be \(x\) and \(103^{\circ}\), and the exterior angle be \(157^{\circ}\). So, \(x + 103^{\circ}=157^{\circ}\).

Step2: Solve for \(x\)

Subtract \(103^{\circ}\) from both sides of the equation \(x+103^{\circ}=157^{\circ}\). We get \(x=157^{\circ}- 103^{\circ}\).

Answer:

\(54^{\circ}\)