Comparing Angular Measurements: Which Angle Has Greater Magnitude?

Angle Comparison with Visual Recognition

Which angle is greatest?

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Step-by-step video solution

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00:00 Which angle is larger?
00:03 According to the drawing, we can see that the left angle is larger
00:06 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Which angle is greatest?

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Step-by-step solution

In drawing A, we can see that the angle is more closed:

While in drawing B, the angle is more open:

In other words, in diagram (a) the angle is more acute, while in diagram (b) the angle is more obtuse.

Remember that the more obtuse an angle is, the larger it is.

Therefore, the larger of the two angles appears in diagram (b).

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Final Answer

Key Points to Remember

Essential concepts to master this topic
  • Rule: Larger angles have wider openings between their rays
  • Technique: Compare how far apart the arms spread from vertex
  • Check: Obtuse angles are always larger than acute angles ✓

Common Mistakes

Avoid these frequent errors
  • Confusing angle size with ray length
    Don't think longer rays make bigger angles = wrong comparison! Ray length doesn't affect angle size - only the opening between rays matters. Always focus on how wide the angle opens, not how long the lines are drawn.

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 just by looking?

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Look at the opening between the two rays! The wider the opening, the larger the angle. Think of it like opening a book - the more you open it, the bigger the angle becomes.

Does the length of the lines affect the angle size?

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No! The angle size depends only on how much the rays are rotated apart from each other. You could draw the lines longer or shorter, but the angle would stay exactly the same size.

What's the difference between acute and obtuse angles?

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An acute angle is smaller than 90° (like a slice of pizza), while an obtuse angle is larger than 90° (like opening a book wide). Obtuse angles are always bigger than acute angles.

Can two angles look the same size but actually be different?

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Yes! Sometimes angles can look very similar, especially when they're close in size. That's why mathematicians use protractors to measure angles precisely when visual comparison isn't enough.

What if I can't tell which angle is bigger?

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Try imagining yourself standing at the vertex (corner) of each angle and looking along one ray, then turning to face the other ray. The angle where you turn more is the larger angle!

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