Question

1. find the value of x. a side of the triangle below has been extended to form an exterior angle of 153°. find the value of x.

Explanation:

Step1: Use the exterior - angle property

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, one of the non - adjacent interior angles is \(90^{\circ}\) (right angle), and the exterior angle is \(153^{\circ}\). Let the other non - adjacent interior angle be \(x\).
We know that \(x + 90^{\circ}=153^{\circ}\) (by the exterior - angle property of a triangle: \( \text{Exterior angle}=\text{Sum of non - adjacent interior angles}\)).

Step2: Solve for \(x\)

Subtract \(90^{\circ}\) from both sides of the equation \(x + 90^{\circ}=153^{\circ}\).
\(x=153^{\circ}-90^{\circ}\)
\(x = 63^{\circ}\)

Answer:

\(63\)