Calculate Angle α in Intersecting Lines with 40° Reference

Q: How do I spot alternate angles in a diagram?

Look for the Z-pattern! Alternate angles are on opposite sides of the line that crosses the parallel lines, and they're on different parallel lines. They form a Z or backwards Z shape.

Q: Are alternate angles always equal?

Yes, but only when the lines are parallel! If the lines aren't parallel, alternate angles won't be equal. Always check that the lines are marked as parallel first.

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

Corresponding angles are in the same position relative to each parallel line (like both top-right). Alternate angles are in different positions - one might be top-left, the other bottom-right.

Q: Why is α = 40° and not something else?

Because $ \alpha $ and the 40° angle form alternate angles. Since the lines are parallel, these alternate angles must be equal, so $ \alpha = 40° $.

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

Look for arrow symbols or identical markings on the lines. The problem statement or diagram should indicate parallel lines. Without parallel lines, you can't use alternate angle properties!

Alternate Angles with Parallel Lines

Calculates the size of the angle $\alpha$

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Step-by-step video solution

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00:00 Find angle A

00:04 Lines are parallel according to the given

00:11 Alternate angles are equal between parallel lines

00:16 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Calculates the size of the angle $\alpha$

Step-by-step solution

Let's review the definition of alternate angles between parallel lines:

Alternate angles are angles located on two different sides of the line that intersects two parallels, and that are also not at the same level with respect to the parallel they are adjacent to. Alternate angles have the same value as each other.

Therefore:

$\alpha=40$

Final Answer

$40$

Key Points to Remember

Essential concepts to master this topic

Rule: Alternate angles between parallel lines are always equal
Technique: Identify the Z-pattern: angles on opposite sides of transversal
Check: Both angles should be on different parallel lines, same value ✓

Common Mistakes

Avoid these frequent errors

Confusing alternate angles with other angle relationships
Don't assume any two angles in the diagram are equal = wrong identification! This leads to using corresponding or co-interior angles incorrectly. Always look for the Z-pattern where angles are on opposite sides of the transversal and on different parallel lines.

Practice Quiz

Test your knowledge with interactive questions

Does the drawing show an adjacent angle?

FAQ

Everything you need to know about this question

How do I spot alternate angles in a diagram?

Look for the Z-pattern! Alternate angles are on opposite sides of the line that crosses the parallel lines, and they're on different parallel lines. They form a Z or backwards Z shape.

Are alternate angles always equal?

Yes, but only when the lines are parallel! If the lines aren't parallel, alternate angles won't be equal. Always check that the lines are marked as parallel first.

What's the difference between alternate and corresponding angles?

Corresponding angles are in the same position relative to each parallel line (like both top-right). Alternate angles are in different positions - one might be top-left, the other bottom-right.

Why is α = 40° and not something else?

Because $\alpha$ and the 40° angle form alternate angles. Since the lines are parallel, these alternate angles must be equal, so $\alpha = 40°$ .

What if I can't see the parallel line markings clearly?

Look for arrow symbols or identical markings on the lines. The problem statement or diagram should indicate parallel lines. Without parallel lines, you can't use alternate angle properties!

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