Question

a side of the triangle below has been extended to form an exterior angle of $145^{circ}$. find the value of $x$.

Explanation:

Step1: Use the exterior - angle property of a triangle

The exterior - angle property of a triangle states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles. Let the right - angle be \(90^{\circ}\). We know that the exterior angle \(E = 145^{\circ}\), and if one of the non - adjacent interior angles is \(x\) and the other is \(90^{\circ}\), then \(E=x + 90^{\circ}\).

Step2: Solve for \(x\)

Rearrange the equation \(145^{\circ}=x + 90^{\circ}\) to isolate \(x\). Subtract \(90^{\circ}\) from both sides of the equation: \(x=145^{\circ}-90^{\circ}\).

Answer:

\(x = 55\)