Question

a side of the triangle below has been extended to form an exterior angle of 156°. find the value of x.
answer attempt 1 out of 2
x=

Explanation:

Step1: Find the adjacent interior angle

The exterior angle and its adjacent interior angle are supplementary. So the adjacent interior angle is \(180^{\circ}- 156^{\circ}=24^{\circ}\).

Step2: Use the triangle angle - sum property

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 \(x\), \(90^{\circ}\), and \(24^{\circ}\). Then \(x + 90^{\circ}+24^{\circ}=180^{\circ}\).

$$x=180^{\circ}-(90^{\circ} + 24^{\circ})$$

$$x=180^{\circ}-114^{\circ}$$

Answer:

\(x = 66\)