Question

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

(there is a diagram showing two parallel lines ( l ) and ( m ), with a triangle between them. one angle in the triangle is ( 39^circ ), another is ( 93^circ ), and the third is ( x^circ ).)

( x = square )

Explanation:

Step1: Use the property of parallel lines (alternate interior angles) and triangle angle sum.

First, the angle adjacent to \(39^\circ\) on line \(l\) and the triangle's angle: since \(l \parallel m\), the alternate interior angle for the \(39^\circ\) angle is equal. Then, in a triangle, the sum of angles is \(180^\circ\). Wait, actually, the angle at the top (on line \(l\)) and the triangle: the angle inside the triangle corresponding to the \(39^\circ\) (alternate interior) and the \(93^\circ\) angle, so we can find \(x\) by \(180 - 39 - 93\)? Wait, no, wait. Wait, the two parallel lines, the triangle has angles: one is \(39^\circ\) (alternate interior, so the base angle of the triangle is \(39^\circ\)), another is \(93^\circ\), so the third angle \(x\) is \(180 - 39 - 93\).

Step2: Calculate \(180 - 39 - 93\)

First, \(39 + 93 = 132\). Then, \(180 - 132 = 48\). So \(x = 48\).

Answer:

\(48\)