Parallel Lines Geometry: Finding Angle α Given 120° Measurement

Question

Lines a and b are parallel.

What is the size of angle α \alpha ?

aaabbb120α

Video Solution

Solution Steps

00:00 Calculate the angle
00:03 The lines are parallel according to the given
00:07 Let's draw a line parallel to our lines
00:16 Corresponding angles are equal between parallel lines
00:26 The angle segment equals all angles minus the right angle
00:33 Alternate angles are equal between parallel lines
00:38 And this is the solution to the question

Step-by-Step Solution

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

aaabbb120α

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:

12090=30 120-90=30

Let's write down the known data as follows:

aaabbbα30

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.

α=30 \alpha=30

Answer

30