Question

a side of the triangle below has been extended to form an exterior angle of 163°. find the value of x.

Explanation:

Step1: Use the exterior angle property of a triangle

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
Let the exterior angle be \(E = 163^{\circ}\), and the two non - adjacent interior angles be \(x\) and \(51^{\circ}\). So, \(E=x + 51^{\circ}\).

Step2: Solve for \(x\)

Rearrange the formula \(x=E - 51^{\circ}\). Substitute \(E = 163^{\circ}\) into the formula: \(x=163^{\circ}-51^{\circ}\).

$$x = 112^{\circ}$$

Answer:

\(112\)