Question

a side of the triangle below has been extended to form an exterior angle of 136°. find the value of x.

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 angles \(90^{\circ}\), \(x^{\circ}\), and the third angle. The exterior angle of \(136^{\circ}\) is equal to the sum of the non - adjacent interior angles \(90^{\circ}\) and \(x^{\circ}\). So, \(136=90 + x\).

Step3: Solve for \(x\)

Subtract \(90\) from both sides of the equation: \(x=136 - 90\).
\(x = 46\)

Answer:

\(46\)