Question

a side of the triangle below has been extended to form an exterior angle of 145°. find the value of x.

Explanation:

Step1: Use the property of supplementary angles

The exterior angle of \(145^{\circ}\) and the adjacent interior angle form a linear - pair (supplementary angles). Let the adjacent interior angle be \(y\). Then \(x + y=180^{\circ}\), so \(y = 180 - 145\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). The triangle has angles \(x\), \(y\), and \(90^{\circ}\). So \(x+y + 90=180\). Since \(y=180 - 145 = 35\), substituting \(y\) into \(x+y + 90=180\) gives \(x+35 + 90=180\). Then \(x=180-(35 + 90)\).
Another way:
Using the exterior - angle property (the exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles). The exterior angle of \(145^{\circ}\) is equal to the sum of the right angle (\(90^{\circ}\)) and \(x\). So \(x+90 = 145\).

Answer:

\(x = 55\)