Question

a side of the triangle below has been extended to form an exterior angle of 153°. 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 \(y + 153^{\circ}=180^{\circ}\), so \(y=180^{\circ}- 153^{\circ}=27^{\circ}\).

Step2: Use the triangle angle - sum property

In a right - triangle (one angle is \(90^{\circ}\)), the sum of the interior angles is \(180^{\circ}\). We know one angle is \(90^{\circ}\) and another (found in Step 1) is \(27^{\circ}\). Let the unknown angle be \(x\). Then \(x + 90^{\circ}+27^{\circ}=180^{\circ}\).
Simplify the equation: \(x=180^{\circ}-(90^{\circ}+27^{\circ})\).
\(x = 180^{\circ}-117^{\circ}\).

Answer:

\(x = 63^{\circ}\)