Find Angle α in Geometric Diagram with 120° Reference

Q: How do I know which angles are corresponding?

Corresponding angles are in the same relative position at each intersection. If one angle is in the upper-right corner at one intersection, its corresponding angle is also upper-right at the other intersection.

Q: Are corresponding angles always equal?

Only when the lines are parallel! If the lines aren't parallel, corresponding angles are not necessarily equal. Always check if parallel lines are given or stated.

Q: Could the answer be 60° instead of 120°?

No! The angle $ \alpha $ is corresponding to the 120° angle, not supplementary. Corresponding angles are equal, so $ \alpha = 120° $.

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

Corresponding angles are on the same side of the transversal in matching positions. Alternate angles are on opposite sides of the transversal. Both are equal when lines are parallel, but they're in different positions.

Corresponding Angles with Parallel Lines

According to the drawing

What is the size of the angle? $\alpha$ ?

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Step-by-step video solution

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00:00 Determine angle A

00:05 According to the given data the lines are parallel

00:12 Corresponding angles between parallel lines are equal

00:21 Here is the solution

Step-by-step written solution

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Understand the problem

According to the drawing

What is the size of the angle? $\alpha$ ?

Step-by-step solution

Given that the angle
$\alpha$ is a corresponding angle to the angle 120 and is also equal to it, therefore $\alpha=120$

Final Answer

$120$

Key Points to Remember

Essential concepts to master this topic

Rule: Corresponding angles formed by parallel lines are always equal
Technique: Identify parallel lines and corresponding angle position: $\alpha = 120°$
Check: Verify angles are in matching positions on parallel lines ✓

Common Mistakes

Avoid these frequent errors

Confusing corresponding angles with other angle relationships
Don't assume angles are alternate interior or supplementary = wrong relationships! This leads to incorrect angle calculations like 60° or 180°. Always identify corresponding angles by their matching positions on parallel lines cut by a transversal.

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 corresponding?

Corresponding angles are in the same relative position at each intersection. If one angle is in the upper-right corner at one intersection, its corresponding angle is also upper-right at the other intersection.

What if the lines don't look parallel in the diagram?

Trust the geometric information given! If the problem states or implies parallel lines, use the parallel line theorems. The diagram may not be drawn to perfect scale.

Are corresponding angles always equal?

Only when the lines are parallel! If the lines aren't parallel, corresponding angles are not necessarily equal. Always check if parallel lines are given or stated.

Could the answer be 60° instead of 120°?

No! The angle $\alpha$ is corresponding to the 120° angle, not supplementary. Corresponding angles are equal, so $\alpha = 120°$ .

What's the difference between corresponding and alternate angles?

Corresponding angles are on the same side of the transversal in matching positions. Alternate angles are on opposite sides of the transversal. Both are equal when lines are parallel, but they're in different positions.

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