Question

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

Explanation:

Step1: Use the exterior angle property

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In a right - angled triangle, one of the interior angles is \(90^{\circ}\). Let the unknown angle be \(x\). The exterior angle is \(149^{\circ}\).
So, \(x + 90^{\circ}=149^{\circ}\)

Step2: Solve for \(x\)

Subtract \(90^{\circ}\) from both sides of the equation:
\(x=149^{\circ}-90^{\circ}\)
\(x = 59^{\circ}\)

Answer:

\(59^{\circ}\)