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?

00:03 Let's find the value of X.

00:06 The problem tells us these lines are parallel.

00:10 Remember, alternate angles between parallel lines are equal.

00:21 Here, we also have alternate angles.

00:28 Angles on a straight line add up to 180 degrees.

00:36 So, we'll add the angles and set them equal to 180 to solve for X.

00:48 Now, let's isolate X to find its value.

01:00 And there you have it! That's how we solve for X.

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°