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

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

646464XXX757575

What is the value of X?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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.

Step-by-step written solution

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1

Understand the problem

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

646464XXX757575

What is the value of X?

2

Step-by-step solution

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 64+x+75=180

x=1807564=41 x=180-75-64=41

3

Final Answer

41°

Practice Quiz

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If one of two corresponding angles is a right angle, then the other angle will also be a right angle.

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