Question

a side of the triangle below has been extended to form an exterior angle of 134°. find the value of x.

Explanation:

Step1: Find the adjacent interior angle

The sum of an exterior angle and its adjacent interior angle is \(180^{\circ}\). Let the adjacent interior angle be \(y\). Then \(y + 134^{\circ}=180^{\circ}\), so \(y = 180^{\circ}- 134^{\circ}=46^{\circ}\).

Step2: Use the triangle angle - sum property

The sum of angles in a triangle is \(180^{\circ}\). In the right - angled triangle, one angle is \(90^{\circ}\), another is \(y = 46^{\circ}\), and the third is \(x\). So \(x+46^{\circ}+90^{\circ}=180^{\circ}\).

$$x=180^{\circ}-(90^{\circ} + 46^{\circ})$$

$$x=180^{\circ}-136^{\circ}$$

$$x = 44^{\circ}$$

Answer:

\(44\)