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 interior angle adjacent to \(149^\circ\) is \(180^\circ - 149^\circ\).
\(180 - 149 = 31^\circ\)

Step2: Use triangle angle sum

A right triangle has one angle \(90^\circ\). Let the unknown angle be \(x\). Then \(x + 90^\circ + 31^\circ = 180^\circ\) (triangle angle sum is \(180^\circ\)).
Solve for \(x\): \(x = 180 - 90 - 31\)
\(x = 59\)

Answer:

\(x = 59\)