Question

a side of the triangle below has been extended to form an exterior angle of 143°. find the value of x.

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In this right - angled triangle, the exterior angle is \(143^{\circ}\), and the two non - adjacent interior angles are \(x^{\circ}\) and \(90^{\circ}\). So, we have the equation \(x + 90=143\).

Step2: Solve for \(x\)

Subtract \(90\) from both sides of the equation \(x + 90=143\).
\(x=143 - 90\)

Answer:

\(x = 53\)