Adjacent Angles Analysis: Can Right and Obtuse Angles Share a Side?

Adjacent Angles with Sum Constraints

Is it possible to have two adjacent angles, one of which is obtuse and the other right?

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Step-by-step video solution

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00:00 Can adjacent angles be one obtuse and one right angle?
00:04 Adjacent angles sum to 180° (straight angle)
00:07 Let's assume one angle is obtuse (greater than 90°)
00:12 And the second is right (equals 90°)
00:18 We can see that the only angle that complements to 180° is a right angle
00:26 Therefore one angle cannot be obtuse and the other right
00:31 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Is it possible to have two adjacent angles, one of which is obtuse and the other right?

2

Step-by-step solution

Remember the definition of adjacent angles:

Adjacent angles always complement each other up to one hundred eighty degrees, that is, their sum is 180 degrees.

This situation is impossible since a right angle equals 90 degrees, an obtuse angle is greater than 90 degrees.

Therefore, together their sum will be greater than 180 degrees.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Rule: Adjacent angles always sum to exactly 180 degrees
  • Technique: Right angle (90°) + obtuse angle (>90°) > 180°
  • Check: Sum must equal 180°; if greater, angles cannot be adjacent ✓

Common Mistakes

Avoid these frequent errors
  • Assuming any two angles can be adjacent
    Don't think any two angles can share a side and be adjacent = wrong geometric relationship! This ignores the fundamental constraint that adjacent angles must sum to exactly 180°. Always check that the angle sum equals 180° before confirming they can be adjacent.

Practice Quiz

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Does the drawing show an adjacent angle?

FAQ

Everything you need to know about this question

What exactly makes two angles adjacent?

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Adjacent angles must share a common side and their measures must add up to exactly 180 degrees. They're like two puzzle pieces that fit together to form a straight line.

Can a right angle be adjacent to any obtuse angle?

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No, never! A right angle is exactly 90°, and obtuse angles are greater than 90°. Since 90° + (greater than 90°) > 180°, they can't be adjacent.

What's the largest angle that can be adjacent to a right angle?

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The largest angle adjacent to a right angle (90°) would be 90 degrees because 90° + 90° = 180°. Anything larger would exceed the 180° requirement.

Are complementary angles the same as adjacent angles?

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No! Complementary angles add up to 90 degrees, while adjacent angles add up to 180 degrees. Don't confuse these two important relationships.

How can I remember the adjacent angle rule?

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Think of adjacent angles as forming a straight line! Since a straight line measures 180°, any two adjacent angles must add up to exactly this amount.

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