Question

question
a side of the triangle below has been extended to form an exterior angle of 126°. 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.
Let the non - adjacent interior angles be \(x\) and \(104^{\circ}\), and the exterior angle be \(126^{\circ}\). So, \(x + 104^{\circ}=126^{\circ}\).

Step2: Solve for \(x\)

Subtract \(104^{\circ}\) from both sides of the equation \(x + 104^{\circ}=126^{\circ}\).
\(x=126^{\circ}-104^{\circ}\)
\(x = 22^{\circ}\)

Answer:

\(22\)