Question

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

Explanation:

Step1: Recall linear pair property

A linear pair of angles sums to \(180^\circ\). So the adjacent interior angle to \(149^\circ\) is \(180^\circ - 149^\circ = 31^\circ\).

Step2: Use triangle angle sum

The triangle is right - angled, so the sum of angles is \(180^\circ\). Let the right angle be \(90^\circ\), the other interior angle be \(31^\circ\), and the angle we need be \(x\). Then \(x+90^\circ + 31^\circ=180^\circ\), so \(x = 180^\circ-(90^\circ + 31^\circ)=59^\circ\).

Answer:

\(x = 59\)