Find X in Parallel Lines: Using 64° and 75° Angles

Question

Look at the angles formed by parallel lines in the figure below:

What is the value of X?

00:00 Find X

00:03 The lines are parallel according to the given

00:07 Alternate angles are equal between parallel lines

00:18 These are also alternate angles

00:25 The sum of angles on a line equals 180

00:33 Let's sum the angles and equate to 180 to find X

00:45 Isolate X

00:57 And this is the solution to the problem

Given that the three lines are parallel:

The 75 degree angle is an alternate angle with the one adjacent to angle X on the right side, and therefore is also equal to 75 degrees.

The 64 degree angle is an alternate angle with the one adjacent to angle X on the left side, and therefore is also equal to 64 degrees.

Now we can calculate:

$64+x+75=180$

$x=180-75-64=41$

41°