Question

a side of the triangle below has been extended to form an exterior angle of 142°. 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 a right - triangle (one of the interior angles is \(90^{\circ}\)), if the exterior angle is \(142^{\circ}\), and let the two non - adjacent interior angles be \(x\) and \(90^{\circ}\). Then \(x + 90^{\circ}=142^{\circ}\).

Step2: Solve for \(x\)

Subtract \(90^{\circ}\) from both sides of the equation \(x + 90^{\circ}=142^{\circ}\). So \(x=142^{\circ}-90^{\circ}\).

Answer:

\(x = 52\)