Calculate Alpha Angle: Using Parallel Lines and 55-Degree Reference

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

Corresponding angles are in the same relative position when a transversal crosses parallel lines - they're equal. Alternate angles are on opposite sides of the transversal and also equal.

Q: Why isn't alpha just 55° if the lines are parallel?

Because $ \alpha $ and the 55° angle are supplementary angles (they form a straight line), not corresponding angles. Supplementary angles add up to 180°, so α = 180° - 55° = 125°.

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 add to 180°, they're supplementary. If they're in matching positions, they're corresponding and equal.

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

The problem states the lines are parallel, so trust that information. Use the angle markings and labels in the diagram to identify relationships, not just visual appearance.

Q: Can I solve this without knowing about parallel lines?

No! The parallel line property is essential. Without it, we can't determine that certain angles are equal or supplementary. Always use the given information about parallel lines.

Parallel Lines with Corresponding Angles

Calculate the angle $\alpha$ given that the lines in the diagram are parallel.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate A

00:03 Parallel lines according to the given data

00:06 Alternate angles between parallel lines are equal

00:09 The angles sum to 180° (supplement to a straight angle)

00:14 Let's sum and equate to 180

00:19 Let's isolate angle A

00:27 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Calculate the angle $\alpha$ given that the lines in the diagram are parallel.

Final Answer

125°

Key Points to Remember

Essential concepts to master this topic

Parallel Lines Rule: Corresponding angles are equal when lines are parallel
Technique: Find angle relationships using 55° reference to calculate $\alpha$
Check: Verify corresponding angles sum to 180° with supplementary angles ✓

Common Mistakes

Avoid these frequent errors

Confusing corresponding angles with alternate angles
Don't assume all angles with parallel lines are equal = wrong 55° answer! Corresponding angles are equal, but supplementary angles add to 180°. Always identify the angle relationship first, then apply the correct rule.

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

What's the difference between corresponding and alternate angles?

Corresponding angles are in the same relative position when a transversal crosses parallel lines - they're equal. Alternate angles are on opposite sides of the transversal and also equal.

Why isn't alpha just 55° if the lines are parallel?

Because $\alpha$ and the 55° angle are supplementary angles (they form a straight line), not corresponding angles. Supplementary angles add up to 180°, so α = 180° - 55° = 125°.

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 add to 180°, they're supplementary. If they're in matching positions, they're corresponding and equal.

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

The problem states the lines are parallel, so trust that information. Use the angle markings and labels in the diagram to identify relationships, not just visual appearance.

Can I solve this without knowing about parallel lines?

No! The parallel line property is essential. Without it, we can't determine that certain angles are equal or supplementary. Always use the given information about parallel lines.

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