Angle Classification: Identifying Obtuse Angles in Geometry

Obtuse Angle Recognition with Visual Analysis

Which of the following angles are obtuse?

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Step-by-step video solution

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00:00 Choose the drawings where an obtuse angle is drawn
00:02 None of the drawings have an obtuse angle (greater than 90)

Step-by-step written solution

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1

Understand the problem

Which of the following angles are obtuse?

2

Step-by-step solution

By definition, an obtuse angle is an angle that is greater than 90 degrees. We can observe that in one drawing there is an angle of 90 degrees and therefore it is not an obtuse angle, the other two angles are less than 90 degrees meaning they are also not obtuse, they are acute angles.

Therefore, none of the answers is correct.

3

Final Answer

None of the options

Key Points to Remember

Essential concepts to master this topic
  • Definition: Obtuse angles measure greater than 90 degrees but less than 180 degrees
  • Visual Check: Compare angle opening to right angle (90°) - wider opening means obtuse
  • Verification: Use angle arc markings and compare to square corner reference ✓

Common Mistakes

Avoid these frequent errors
  • Confusing acute angles with obtuse angles
    Don't assume wider-looking angles are automatically obtuse = wrong classification! An angle might appear large but still be less than 90°. Always compare the angle opening to a perfect right angle (90°) as your reference point.

Practice Quiz

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Which of the following angles is a plane angle?

FAQ

Everything you need to know about this question

How can I tell if an angle is obtuse just by looking?

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Look for an angle that opens wider than a right angle (like the corner of a square). If the angle looks like it could fit a right angle inside it with room left over, it's obtuse!

What's the difference between obtuse and acute angles?

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Acute angles are less than 90° (sharp and narrow), while obtuse angles are greater than 90° (wide and blunt). Think: acute = cute and small, obtuse = big and wide.

Can a straight line be an obtuse angle?

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No! A straight line measures exactly 180° 180° , which makes it a straight angle, not obtuse. Obtuse angles are between 90° and 180°.

Why do none of the options show obtuse angles?

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The first angle is exactly 90° (right angle), and the second appears to be acute (less than 90°). Since no angle exceeds 90°, none qualify as obtuse.

How do I measure angles without a protractor?

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Use visual comparison! Compare to familiar references:

  • Right angle: corner of paper or book
  • Acute: smaller than corner
  • Obtuse: wider than corner

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