Question

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

Explanation:

Step1: Find the alternate - interior angle

Since \( l\parallel m \), the angle adjacent to \( 113^{\circ} \) (let's call it \( y \)) satisfies \( y + 113^{\circ}=180^{\circ} \) (linear - pair). So \( y = 180^{\circ}-113^{\circ}=67^{\circ} \).

Step2: Use the property of parallel lines and transversal for the \( 33^{\circ} \) angle

The angle equal to \( 33^{\circ} \) (by alternate - interior angles) and \( x^{\circ} \) and \( y^{\circ} \) are related. We know that \( x + 33=y \) (by the property of angles formed by a transversal cutting parallel lines).
Substitute \( y = 67^{\circ} \) into \( x + 33=y \). Then \( x=67 - 33 \).

Answer:

\( x = 34 \)