Question

a side of the triangle below has been extended to form an exterior angle of 124°. 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 \(124^\circ\) is \(180^\circ - 124^\circ\).
\(180 - 124 = 56^\circ\)

Step2: Use triangle angle sum (right triangle)

The triangle is right - angled, so the sum of non - right angles is \(90^\circ\). Let the right angle be \(90^\circ\), one angle is \(56^\circ\), and the other is \(x\). So \(x+56 = 90\) (since in a right triangle, the two non - right angles are complementary).
\(x=90 - 56\)
\(x = 34\)

Answer:

\(34^\circ\)