Question

a side of the triangle below has been extended to form an exterior angle of 126°. find the value of x.
(there is a right triangle in the image, with one angle marked x° and an exterior angle of 126° at the adjacent side extension.)
answer attempt 1 out of 2
x = input box submit answer

Explanation:

Step1: Use the exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let the right - angled triangle have angles \(x\), \(90^{\circ}\), and the non - adjacent interior angle related to the exterior angle \(126^{\circ}\). According to the exterior angle theorem, \(126^{\circ}=x + 90^{\circ}\).

Step2: Solve for \(x\)

Subtract \(90^{\circ}\) from both sides of the equation \(126^{\circ}=x + 90^{\circ}\). So, \(x=126^{\circ}-90^{\circ}\).

Answer:

\(x = 36\)