Question

in the figure below, l || m. find x.

Explanation:

Step1: Use angle - sum property of triangle

The sum of interior angles of a triangle is 180°.

Step2: Calculate the third - angle value

Let the third angle of the triangle be \(y\). Since \(l\parallel m\), the angle corresponding to \(67^{\circ}\) and the third - angle \(y\) of the triangle are equal. So \(y = 67^{\circ}\).
We know that \(x + 33^{\circ}+y=180^{\circ}\). Substituting \(y = 67^{\circ}\) into the equation, we get \(x+33^{\circ}+67^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

\(x+100^{\circ}=180^{\circ}\), then \(x=180^{\circ}- 100^{\circ}\).

Answer:

\(x = 80\)