Question

in the figure below, l || m. find x.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°.

Step2: Set up the equation

Let's consider the triangle formed. We know two angles of the triangle are 45° and 96°. Let the third angle be \(y\). So, \(y + 45+96 = 180\).
\[y=180-(45 + 96)=180 - 141=39\]

Step3: Use the property of parallel lines

Since \(l\parallel m\), the angle \(x\) and the angle \(y\) are alternate - interior angles. Alternate - interior angles formed by two parallel lines and a transversal are equal. So \(x=y\).

Answer:

39