Question

a side of the triangle below has been extended to form an exterior angle of 133°. find the value of x.

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an 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 let the other non - adjacent interior angle be \(y\). So, \(133^{\circ}=90^{\circ}+y\). Solving for \(y\), we get \(y = 133^{\circ}-90^{\circ}=43^{\circ}\).

Step2: Use the linear - pair relationship

Since \(x\) and \(y\) form a linear pair (they are adjacent angles on a straight line), \(x + y=180^{\circ}\). Substituting \(y = 43^{\circ}\) into the equation, we have \(x+43^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Subtract \(43^{\circ}\) from both sides of the equation \(x+43^{\circ}=180^{\circ}\). So, \(x=180^{\circ}-43^{\circ}\).

Answer:

\(x = 43\)