Question

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

Explanation:

Step1: Use alternate - interior angles property

Since the two lines are parallel, the alternate - interior angles are equal. Let's assume the angle corresponding to the given non - x angles are equal due to parallel lines. The sum of angles around a point is 360 degrees. The two non - x angles are 40 degrees and 137 degrees.

Step2: Calculate the sum of known angles

The sum of the two non - x angles is \(40 + 137=177\) degrees.

Step3: Find the value of x

We know that \(x + x+177 = 360\) (sum of angles around a point). Combining like terms, we get \(2x=360 - 177\). So \(2x = 183\), and \(x=\frac{183}{2}=91.5\) degrees.

Answer:

\(x = 91.5\) degrees