Question

a side of the triangle below has been extended to form an exterior angle of 164°. find the value of x.

Explanation:

Step1: Find the adjacent interior angle

The adjacent interior angle \( y \) and the exterior angle \( 164^{\circ} \) are supplementary. So \( y=180 - 164=16^{\circ} \)

Step2: Use the triangle angle - sum property

The sum of angles in a triangle is \( 180^{\circ} \). Let the angles of the triangle be \( y = 16^{\circ}\), \(112^{\circ}\), and \(x\). Then \(x+16 + 112=180\)

$$x=180-(16 + 112)$$

$$x=180 - 128$$

$$x = 52$$

Answer:

\(52\)