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

Parallel Lines with Alternate Interior 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

Follow each step carefully to understand the complete solution
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°

Key Points to Remember

Essential concepts to master this topic
  • Parallel Lines Rule: Corresponding and alternate angles are always equal
  • Technique: Set up equation 64+x+75=180 64 + x + 75 = 180 using angle sum
  • Check: Verify 64+41+75=180 64 + 41 + 75 = 180 degrees ✓

Common Mistakes

Avoid these frequent errors
  • Not identifying alternate interior angles correctly
    Don't assume any angles are equal without checking their relationship = wrong calculations! Students often confuse vertical angles with alternate angles. Always identify which angles are alternate interior first, then apply the parallel lines rule that alternate interior angles are equal.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

How do I know which angles are alternate interior?

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Alternate interior angles are on opposite sides of the transversal and between the parallel lines. They form a "Z" pattern when you trace them!

Why do the three angles add up to 180°?

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The three angles form a straight line, and angles on a straight line always sum to 180 degrees. This is true regardless of parallel lines!

What if I can't see the parallel lines clearly?

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Look for the parallel line symbols (arrows) in the diagram, or read the problem statement. The question will always tell you when lines are parallel!

Can I solve this without using alternate angles?

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You need to use the parallel lines property to find the unknown angles first. Without knowing that alternate interior angles are equal, you can't set up the equation 64+x+75=180 64 + x + 75 = 180 .

What if my answer doesn't make sense?

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Check that your answer is positive and less than 180° for individual angles. Also verify that 64+41+75=180 64 + 41 + 75 = 180 exactly!

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