Question

a side of the triangle below has been extended to form an exterior angle of 154°. find the value of x.

Explanation:

Step1: Use the exterior - angle property of a triangle

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In a right - angled triangle (one angle is \(90^{\circ}\)), if the exterior angle is \(154^{\circ}\), and let the other non - adjacent interior angle be \(x\). Then, by the exterior - angle formula \(154^{\circ}=x + 90^{\circ}\).

Step2: Solve for \(x\)

Subtract \(90^{\circ}\) from both sides of the equation \(x=154^{\circ}-90^{\circ}\).

Answer:

\(x = 64\)