Question

in the figure below, ( l parallel m ). find ( x ).

Explanation:

Step1: Use the property of parallel lines

When two parallel lines \(l\parallel m\), the alternate - interior angles are equal. Let's assume the angle formed by the transversal with line \(l\) and the given \(33^{\circ}\) angle has a corresponding relationship.

Step2: Apply the angle - sum property

We know that if we consider the angles on the same side of the transversal between the parallel lines \(l\) and \(m\), we can use the fact that the sum of angles formed by a transversal with two parallel lines (in a certain configuration) gives us an equation.
Since \(l\parallel m\), we have \(33^{\circ}+x^{\circ}=80^{\circ}\) (by the property of alternate - interior angles and angle addition).

Step3: Solve for \(x\)

Subtract \(33^{\circ}\) from both sides of the equation \(x = 80 - 33\).

Answer:

\(x = 47\)