Question

a side of the triangle below has been extended to form an exterior angle of 149°. find the value of x.

Explanation:

Step1: Identify adjacent interior angle

The exterior angle and its adjacent interior angle are supplementary (sum to \(180^\circ\)). Let the adjacent interior angle be \(y\). So, \(y + 149^\circ = 180^\circ\). Solving for \(y\), we get \(y = 180^\circ - 149^\circ = 31^\circ\).

Step2: Use triangle angle sum

The triangle is right - angled, so one angle is \(90^\circ\). The sum of angles in a triangle is \(180^\circ\). So, \(x + 90^\circ + y = 180^\circ\). We know \(y = 31^\circ\), substitute it in: \(x+90^\circ + 31^\circ=180^\circ\). Then \(x=180^\circ-(90^\circ + 31^\circ)=180^\circ - 121^\circ = 59^\circ\).

Answer:

\(x = 59\)