Calculate Angle α: Parallel Lines with 120° Intersection Problem

Q: Why isn't the answer 120°?

The 120° angle and α are supplementary, not equal! They're on the same straight line, so they must add up to 180°. That's why α = 180° - 120° = 60°.

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

Look at the position of the angles! Are they in the same relative position (corresponding), on opposite sides (alternate), or on the same line (supplementary)? The diagram shows α and 120° are supplementary.

Q: Are there other ways to solve this?

Yes! You could use alternate interior angles or corresponding angles depending on how you label the diagram. All methods with parallel lines will give α = 60°.

Q: How can I remember all these angle rules?

Corresponding: Same position, equal anglesAlternate: Opposite sides, equal anglesSupplementary: Same line, angles add to 180°Practice identifying the relationship first, then apply the rule!

Parallel Lines with Transversal Angle Relationships

Calculate the angle $\alpha$ 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 Calculate A

00:04 Parallel lines according to the given

00:08 Alternate angles are equal between parallel lines

00:11 The angles sum to 180 (supplement to a straight angle)

00:19 Isolate A

00:22 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 below are parallel.

Final Answer

60°

Key Points to Remember

Essential concepts to master this topic

Rule: Parallel lines cut by transversal create equal corresponding angles
Technique: Find supplementary angle: 180° - 120° = 60°
Check: Corresponding angles are equal: α = 60° ✓

Common Mistakes

Avoid these frequent errors

Thinking α equals the given angle directly
Don't assume α = 120° just because it's the marked angle! This ignores angle relationships and gives the wrong answer. Always identify whether angles are corresponding, alternate, or supplementary first.

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

Why isn't the answer 120°?

The 120° angle and α are supplementary, not equal! They're on the same straight line, so they must add up to 180°. That's why α = 180° - 120° = 60°.

How do I know which angle relationship to use?

Look at the position of the angles! Are they in the same relative position (corresponding), on opposite sides (alternate), or on the same line (supplementary)? The diagram shows α and 120° are supplementary.

What if the lines weren't parallel?

If lines aren't parallel, these special angle relationships don't work! Corresponding and alternate angles are only equal when lines are parallel. Always check this condition first.

Are there other ways to solve this?

Yes! You could use alternate interior angles or corresponding angles depending on how you label the diagram. All methods with parallel lines will give α = 60°.

How can I remember all these angle rules?

Corresponding: Same position, equal angles
Alternate: Opposite sides, equal angles
Supplementary: Same line, angles add to 180°

Practice identifying the relationship first, then apply the rule!

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