Question

a side of the triangle below has been extended to form an exterior angle of 68°. find the value of x.

Explanation:

Step1: Recall 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. Let's denote the exterior angle as \(E = 68^{\circ}\), one non - adjacent interior angle as \(47^{\circ}\) and the other non - adjacent interior angle as \(x^{\circ}\).

Step2: Apply the exterior angle theorem

According to the exterior angle theorem, we have the equation \(68=47 + x\).
To solve for \(x\), we subtract \(47\) from both sides of the equation: \(x=68 - 47\).

Step3: Calculate the value of \(x\)

\(68-47 = 21\). So \(x = 21\).

Answer:

\(x = 21\)