Question

a side of the triangle below has been extended to form an exterior angle of 64°. find the value of x.

Explanation:

Step1: Recall the exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let's denote the exterior angle as \(64^{\circ}\), one non - adjacent interior angle as \(49^{\circ}\) and the other non - adjacent interior angle as \(x^{\circ}\). So we have the equation \(x + 49=64\).

Step2: Solve for x

To find the value of \(x\), we subtract \(49\) from both sides of the equation \(x + 49=64\).
\(x=64 - 49\)
\(x = 15\)

Answer:

\(15\)