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 sum of the interior angles on the same side of the transversal is \(180^{\circ}\). Let's assume the three - angle sum ( \(50^{\circ}\), \(101^{\circ}\), and the angle adjacent to \(x^{\circ}\) on line \(m\)) and the angle \(x^{\circ}\) follow the alternate - interior angle property.
We know that if we consider a transversal cutting the parallel lines \(l\) and \(m\), the angle \(x\) and the angle formed by the sum of \(180^{\circ}-(50^{\circ} + 101^{\circ})\) are equal (alternate - interior angles).
First, calculate \(50^{\circ}+101^{\circ}=151^{\circ}\).

Step2: Find the value of \(x\)

Since the sum of angles on a straight line is \(180^{\circ}\), the angle adjacent to the sum of \(50^{\circ}\) and \(101^{\circ}\) on line \(m\) is \(180^{\circ}-(50^{\circ}+101^{\circ})\). And because \(l\parallel m\), \(x = 180-(50 + 101)\) (alternate - interior angles).

$$x=180-(50 + 101)=180 - 151=29$$

Answer:

\(29\)