Question

a side of the triangle below has been extended to form an exterior angle of 147°. 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.
Let the right - angle be 90°. The exterior angle is 147°, and one of the non - adjacent interior angles is \(x\) and the other is 90°.
So, \(x + 90^{\circ}=147^{\circ}\).

Step2: Solve for \(x\)

Subtract 90° from both sides of the equation \(x + 90^{\circ}=147^{\circ}\).
\(x=147^{\circ}-90^{\circ}\).
\(x = 57^{\circ}\)

Answer:

\(57\)