Supplementary Angles Proof: Is Alpha + Beta = 180 Degrees?

Q: How do I know if two angles are supplementary?

Two angles are supplementary when they add up to 180°. In this diagram, α and β share a vertex and their non-common sides form a straight line, making them supplementary.

Q: What's the difference between adjacent and supplementary angles?

Adjacent angles share a vertex and side but don't overlap. Supplementary angles add to 180°. These angles are both adjacent AND supplementary because they form a linear pair!

Q: How do I prove this is true?

Use the Linear Pair Postulate: If two angles form a linear pair (adjacent angles whose non-common sides form a straight line), then they are supplementary and sum to $ 180° $.

Supplementary Angles with Linear Pair Properties

True or false?

$\alpha+\beta=180$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine whether the angles add up to 180 degrees

00:03 The angles are on the same line and are intersected by the same leg

00:06 Therefore they are adjacent angles, adjacent angles add up to 180 degrees

00:10 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

True or false?

$\alpha+\beta=180$

Step-by-step solution

Given that the angles alpha and beta are on the same straight line and given that they are adjacent angles. Together they are equal to 180 degrees and the statement is true.

Final Answer

True

Key Points to Remember

Essential concepts to master this topic

Linear Pair Rule: Adjacent angles on a straight line sum to 180°
Technique: Identify angles sharing a common vertex and side on line
Check: Verify angles are adjacent and form straight line = 180° ✓

Common Mistakes

Avoid these frequent errors

Assuming any two angles equal 180°
Don't assume α + β = 180° just because they're labeled angles = wrong conclusion! This ignores their position and relationship. Always verify the angles are adjacent and form a linear pair on a straight line.

Practice Quiz

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Can a triangle have two right angles?

FAQ

Everything you need to know about this question

How do I know if two angles are supplementary?

Two angles are supplementary when they add up to 180°. In this diagram, α and β share a vertex and their non-common sides form a straight line, making them supplementary.

What's the difference between adjacent and supplementary angles?

Adjacent angles share a vertex and side but don't overlap. Supplementary angles add to 180°. These angles are both adjacent AND supplementary because they form a linear pair!

Can angles be supplementary without being adjacent?

Yes! Any two angles that add to 180° are supplementary, even if they're in different locations. But when they're adjacent on a straight line, we call them a linear pair.

What if the angles don't look like they add to 180°?

Don't judge by appearance! If the diagram shows angles on a straight line, they mathematically must add to 180°. The visual can be misleading due to scale.

How do I prove this is true?

Use the Linear Pair Postulate: If two angles form a linear pair (adjacent angles whose non-common sides form a straight line), then they are supplementary and sum to $180°$ .

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