Find X Using Parallel Lines: Solving 2X and 8X-40 Angle Relationship

Q: How do I know which angles are equal?

Corresponding angles are in the same relative position when a transversal crosses parallel lines. Look for angles in matching corners - they're always equal!

Q: What if I get a fraction for X?

Fractions are perfectly valid answers! Just make sure to simplify and check your work by substituting back into both angle expressions.

Q: Should the angles add up to 180°?

Not always! Corresponding angles are equal, while co-interior angles add to 180°. Check the diagram carefully to identify which relationship applies.

Q: How can I verify my answer is correct?

Substitute your X value back into both expressions. If 2X = 8X - 40 gives the same angle measure on both sides, you're right!

Parallel Lines with Angle Relationships

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

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Step-by-step video solution

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00:00 Find X

00:03 Corresponding angles are equal between parallel lines

00:08 Angles that sum to 180° form a straight angle

00:11 Isolate X

00:16 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

Rule: Corresponding angles are equal when lines are parallel
Technique: Set angle expressions equal: 2X = 8X - 40
Check: Substitute X = 22/3 back into both expressions ✓

Common Mistakes

Avoid these frequent errors

Confusing angle relationships with parallel lines
Don't assume angles are supplementary when they're actually corresponding angles = wrong equation setup! Corresponding angles are equal, not adding to 180°. Always identify the angle relationship first based on position.

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 equal?

Corresponding angles are in the same relative position when a transversal crosses parallel lines. Look for angles in matching corners - they're always equal!

What if I get a fraction for X?

Fractions are perfectly valid answers! Just make sure to simplify and check your work by substituting back into both angle expressions.

Should the angles add up to 180°?

Not always! Corresponding angles are equal, while co-interior angles add to 180°. Check the diagram carefully to identify which relationship applies.

How can I verify my answer is correct?

Substitute your X value back into both expressions. If 2X = 8X - 40 gives the same angle measure on both sides, you're right!

What if my algebra gives a negative angle?

Check your work! Angles in geometry problems are typically positive. A negative result usually means an error in setting up or solving the equation.

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