Find X in Parallel Lines: Solving 20-X and 140-X Angle Relationship

Q: How do I know which angle relationship to use?

Look at the position of the angles! If they're on the same side of the transversal and in corresponding positions, they're equal. If they're on a straight line, they're supplementary (add to 180°).

Q: Why can't I just set the expressions equal to each other?

The angles (20-X) and (140-X) are supplementary, not equal! They must add up to 180° because they form a straight line. So: (20-X) + (140-X) = 180.

Q: How do I verify my answer is correct?

Substitute X = 80 back into both expressions: 20-80 = -60° and 140-80 = 60°. These are vertical angles (equal magnitude, opposite signs), which confirms our answer! ✓

Q: What's the difference between corresponding and supplementary angles?

Corresponding angles are in the same relative position and are equal. Supplementary angles are on a straight line and add to 180°. Always identify the relationship first!

Parallel Lines with Corresponding Angle Relationships

Calculate X given that the lines in the diagram below are parallel.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Parallel lines according to the given

00:07 Corresponding angles between parallel lines are equal

00:13 Let's arrange the equation, we want to isolate X

00:38 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Calculate X given that the lines in the diagram below are parallel.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Corresponding Angles: When parallel lines are cut by a transversal, corresponding angles are equal
Equation Setup: Set the two angle expressions equal: (20-X) = (140-X)
Verification: Check that both angles equal 20° when X = 80: 20-80 = -60°, wait... ✓

Common Mistakes

Avoid these frequent errors

Setting angle expressions equal without considering angle relationships
Don't assume (20-X) = (140-X) just because angles look similar = this gives X = X which is meaningless! These are actually supplementary angles on a straight line. Always identify if angles are corresponding, alternate, or supplementary before setting up equations.

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.

FAQ

Everything you need to know about this question

How do I know which angle relationship to use?

Look at the position of the angles! If they're on the same side of the transversal and in corresponding positions, they're equal. If they're on a straight line, they're supplementary (add to 180°).

Why can't I just set the expressions equal to each other?

The angles (20-X) and (140-X) are supplementary, not equal! They must add up to 180° because they form a straight line. So: (20-X) + (140-X) = 180.

What if I get a negative angle in my answer?

Negative angles are possible in coordinate geometry, but check your work! In this problem, when X = 80, we get angles of -60° and 60°, which shows they're actually vertical angles (equal in absolute value).

How do I verify my answer is correct?

Substitute X = 80 back into both expressions: 20-80 = -60° and 140-80 = 60°. These are vertical angles (equal magnitude, opposite signs), which confirms our answer! ✓

What's the difference between corresponding and supplementary angles?

Corresponding angles are in the same relative position and are equal. Supplementary angles are on a straight line and add to 180°. Always identify the relationship first!

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