Calculate Angle α in Intersecting Lines with 72° Given Angle

Q: What exactly are vertical angles?

Vertical angles are the opposite angles formed when two lines intersect. They're called 'vertical' because they share the same vertex (intersection point), not because they're up and down!

Q: How do I identify which angles are vertical?

Look for angles that are directly opposite each other across the intersection point. They don't share a side - there's empty space between them with the intersection in the middle.

Q: Could α be 108° instead of 72°?

No! 108° would be the measure of an adjacent angle (next to the 72°). Since 72° + 108° = 180°, those would be supplementary angles, not vertical angles.

Q: Do I need to use any formulas for this?

Not really! Just remember the vertical angles theorem: vertical angles are equal. So if one vertical angle is 72°, its opposite angle is also 72°.

Vertical Angles with Intersecting Lines

Calculate the angle $\alpha$

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Step-by-step video solution

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00:00 Find angle A

00:03 Lines are parallel according to the given

00:11 Corresponding angles between parallel lines are equal

00:17 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Calculate the angle $\alpha$

Final Answer

$72$

Key Points to Remember

Essential concepts to master this topic

Vertical Angles Rule: Opposite angles formed by intersecting lines are equal
Angle Identification: The 72° and α are vertical angles across intersection
Verification: Check that α = 72° by confirming angles are opposite ✓

Common Mistakes

Avoid these frequent errors

Confusing vertical angles with adjacent angles
Don't assume α is supplementary to 72° (adding to 180°) = wrong answer of 108°! Adjacent angles are supplementary, but vertical angles are opposite each other across the intersection. Always identify which angles are directly across from each other.

Practice Quiz

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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 exactly are vertical angles?

Vertical angles are the opposite angles formed when two lines intersect. They're called 'vertical' because they share the same vertex (intersection point), not because they're up and down!

Why are vertical angles always equal?

When two lines intersect, they create four angles. The angles next to each other are supplementary (add to 180°), but the angles across from each other are equal because they're formed by the same pair of intersecting lines.

How do I identify which angles are vertical?

Look for angles that are directly opposite each other across the intersection point. They don't share a side - there's empty space between them with the intersection in the middle.

Could α be 108° instead of 72°?

No! 108° would be the measure of an adjacent angle (next to the 72°). Since 72° + 108° = 180°, those would be supplementary angles, not vertical angles.

Do I need to use any formulas for this?

Not really! Just remember the vertical angles theorem: vertical angles are equal. So if one vertical angle is 72°, its opposite angle is also 72°.

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