Question

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

Explanation:

Step1: Find the alternate - interior angle

Since \(l\parallel m\), the alternate - interior angle of \(33^{\circ}\) is \(33^{\circ}\). The angle adjacent to \(113^{\circ}\) is \(180 - 113=67^{\circ}\) (linear pair).

Step2: Use the triangle - angle sum property

In a triangle, the sum of interior angles is \(180^{\circ}\). Let the angles of the triangle be \(33^{\circ}\), \(x^{\circ}\), and \(67^{\circ}\). Then \(33 + x+67 = 180\).
Simplify the left - hand side: \(x+100 = 180\).
Subtract 100 from both sides: \(x=180 - 100\).

Answer:

\(x = 80\)