Question

a side of the triangle below has been extended to form an exterior angle of 76°. 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 the interior angle adjacent to the \(76^{\circ}\) exterior angle be \(y\). Then \(y + 76^{\circ}=180^{\circ}\) (linear pair), so \(y = 180^{\circ}- 76^{\circ}=104^{\circ}\). But we can also use the exterior angle theorem directly. The exterior angle (\(76^{\circ}\)) is equal to the sum of the two non - adjacent interior angles (\(x\) and \(51^{\circ}\)). So we have the equation \(x + 51^{\circ}=76^{\circ}\).

Step2: Solve for \(x\)

To find \(x\), we subtract \(51^{\circ}\) from both sides of the equation \(x+51^{\circ}=76^{\circ}\).
\(x=76^{\circ}- 51^{\circ}\)
\(x = 25^{\circ}\)

Answer:

\(25\)