Parallel Lines Geometry: Finding Angle α Given 120° Measurement

Lines a and b are parallel.

What is the size of angle $\alpha$?

First, let's draw another line parallel to the existing lines that will divide the given angle of 120 degrees in the following way:

Note that the line we drew creates two adjacent and straight angles, each equal to 90 degrees.

Now we can calculate the missing part of the angle known to us using the formula:

$120-90=30$

Let's write down the known data as follows:

Note that from the drawing we can see that angle alpha and the angle equal to 30 degrees are alternate angles, therefore they are equal to each other.

$\alpha=30$