Question

in the figure below, ( l parallel m ). find ( x ).
figure of two parallel lines ( l ) and ( m ) with a triangle between them, angles 93° and 39° marked, and ( x^circ ) angle at line ( l )
( x = square )

Explanation:

Step1: Find the third angle of the triangle

The sum of angles in a triangle is \(180^\circ\). So the third angle \(y\) (let's call it) is \(180 - 93 - 39\).
\(180 - 93 - 39 = 48^\circ\)

Step2: Use alternate interior angles (since \(l \parallel m\))

The angle \(x\) and the third angle of the triangle are alternate interior angles, so they are equal. Thus, \(x = 48\).

Answer:

\(48\)