Question

a side of the triangle below has been extended to form an exterior angle of 131°. find the value of x.
answer

Explanation:

Step1: Recall exterior - angle property

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.

Step2: Set up the equation

Let the right - angled triangle have non - adjacent interior angles \(x\) and \(90^{\circ}\), and the exterior angle is \(131^{\circ}\). So, \(x + 90^{\circ}=131^{\circ}\).

Step3: Solve for \(x\)

Subtract \(90^{\circ}\) from both sides of the equation: \(x=131^{\circ}-90^{\circ}\).
\(x = 41^{\circ}\)

Answer:

\(41\)