Question

a side of the triangle below has been extended to form an exterior angle of 128°. find the value of x.

Explanation:

Step1: Find adjacent interior angle

$x + 128^\circ = 180^\circ$
$x = 180^\circ - 128^\circ = 52^\circ$

Step2: Verify with triangle angle sum

The triangle is right-angled ($90^\circ$), so the third angle is $180^\circ - 90^\circ - 52^\circ = 38^\circ$, which confirms $x$ is correct as the exterior angle equals the sum of the two non-adjacent interior angles: $90^\circ + 38^\circ = 128^\circ$.

Answer:

$52$