Question

a side of the triangle below has been extended to form an exterior angle of 143°. find the value of x.

Explanation:

Step1: Use the linear - pair relationship

The exterior angle of \(143^{\circ}\) and the interior angle adjacent to it form a linear pair. So the adjacent interior angle \(y = 180^{\circ}-143^{\circ}\).
$$y=180 - 143=37^{\circ}$$

Step2: Use the angle - sum property of a triangle

In a right - triangle (one angle is \(90^{\circ}\)), the sum of the interior angles is \(180^{\circ}\). Let the angles of the triangle be \(90^{\circ}\), \(y = 37^{\circ}\), and \(x\). Then \(90 + 37+x=180\).
$$x=180-(90 + 37)$$
$$x=180 - 127$$
$$x = 53$$

Answer:

\(x = 53\)