Angle Comparison: Determining the Greater Angle in Geometric Analysis

Angle Measurement with Visual Comparison

Indicates which angle is greater

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Step-by-step video solution

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00:02 Which angle is bigger?
00:05 Look at the drawing. The angle is obtuse, so it's larger than ninety degrees.
00:10 And that's the solution to our question.

Step-by-step written solution

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1

Understand the problem

Indicates which angle is greater

2

Step-by-step solution

Note that in drawing B, the two lines form a right angle, which is an angle of 90 degrees:

While the angle in drawing A is greater than 90 degrees:

Therefore, the angle in drawing A is larger.

3

Final Answer

Key Points to Remember

Essential concepts to master this topic
  • Reference: A right angle measures exactly 90 degrees
  • Technique: Compare angles to 90°: obtuse > 90°, acute < 90°
  • Check: Verify by measuring arc size between rays ✓

Common Mistakes

Avoid these frequent errors
  • Confusing angle size with line length
    Don't judge angle size by how long the lines are = wrong comparison! Line length doesn't determine angle measure - only the opening between rays matters. Always focus on the arc between the two rays, not the ray lengths.

Practice Quiz

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Indicates which angle is greater

FAQ

Everything you need to know about this question

How can I tell which angle is bigger without measuring?

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Look at the opening between the two rays! A wider opening means a larger angle. Compare it to a right angle (90°) - if it opens wider than a square corner, it's obtuse and greater than 90°.

What's the difference between acute, right, and obtuse angles?

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Acute angles are less than 90° (sharp), right angles are exactly 90° (square corner), and obtuse angles are greater than 90° (wide opening).

Does the length of the lines affect the angle size?

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No! The angle size depends only on the amount of rotation between the two rays. You could extend or shorten the lines without changing the angle measurement at all.

How do I identify a right angle in a drawing?

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Look for a square symbol in the corner where the lines meet. This small square indicates exactly 90°. Without the symbol, look for lines that appear perpendicular (forming an 'L' shape).

What if both angles look almost the same size?

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Use a reference! Compare both angles to a right angle (90°). One might be slightly acute (less than 90°) while the other is slightly obtuse (more than 90°), making the obtuse one larger.

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