Adjacent Angles Property: Proving Acute and Obtuse Relationships

Adjacent Angles with Sum Properties

If two adjacent angles are not equal to one another, then one of them is obtuse and the other is acute.

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1

Understand the problem

If two adjacent angles are not equal to one another, then one of them is obtuse and the other is acute.

2

Step-by-step solution

The answer is correct because the sum of two acute angles will be less than 180 degrees and the sum of two obtuse angles will be greater than 180 degrees

3

Final Answer

True

Key Points to Remember

Essential concepts to master this topic
  • Rule: Adjacent angles always sum to 180 degrees (supplementary)
  • Technique: If one angle is 120°, the other is 60° (180° - 120°)
  • Check: Verify acute + obtuse = 180°: 60° + 120° = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Assuming adjacent angles can both be acute or both obtuse
    Don't think adjacent angles can both be 70° and 80° = 150° ≠ 180°! Adjacent angles must sum to exactly 180°, so if they're unequal, one must be less than 90° (acute) and one must be greater than 90° (obtuse). Always check that unequal adjacent angles have one acute and one obtuse.

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

Can two adjacent angles both be acute?

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No! If both angles were acute (less than 90°), their sum would be less than 180°. Since adjacent angles must sum to exactly 180 degrees, one must be acute and one obtuse when they're unequal.

What if the adjacent angles are equal?

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If adjacent angles are equal and sum to 180°, then each angle is 90°. These are called right angles - neither acute nor obtuse, but exactly 90°!

Can two adjacent angles both be obtuse?

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Impossible! Two obtuse angles (each greater than 90°) would sum to more than 180°. Since adjacent angles must equal exactly 180°, only one can be obtuse.

How do I remember which angle is acute and which is obtuse?

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Think of it this way: if angles are unequal and sum to 180°, the smaller one is acute (less than 90°) and the larger one is obtuse (greater than 90°).

What's the key property I need to remember?

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Adjacent angles are supplementary - they always add up to 180°. This is the fundamental rule that makes the statement in the question true!

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