Angle Comparison: Determining the Greater Angular Magnitude

Q: How can I tell which angle is bigger just by looking?

Look at the opening between the two rays! The angle with the wider opening is larger. Think of it like opening a door - a wider door opening means a bigger angle.

Q: Do the ray lengths matter when comparing angles?

No! Ray length has nothing to do with angle size. You can extend or shorten rays without changing the angle. Only the opening between rays determines angle measurement.

Q: What's the difference between acute and obtuse angles?

Acute angles are less than 90° (narrow opening), while obtuse angles are greater than 90° (wide opening). Right angles are exactly 90°.

Q: Can I measure these angles without a protractor?

You can estimate by comparing to a right angle (90°). If an angle looks narrower than a square corner, it's acute. If wider, it's obtuse.

Angle Measurement with Visual Comparison

Which angle is greater?

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Step-by-step video solution

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00:00 Indicate 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 greater?

Step-by-step solution

The angle in diagram (a) is more acute, meaning it is smaller:

Conversely, the angle in diagram (b) is more obtuse, making it larger.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Visual Rule: Wider opening between rays indicates larger angle measure
Technique: Compare angle openings: acute < 90°, obtuse > 90°
Check: Red shading shows angle B is wider than angle A ✓

Common Mistakes

Avoid these frequent errors

Assuming longer rays create larger angles
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 rays extend.

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?

Look at the opening between the two rays! The angle with the wider opening is larger. Think of it like opening a door - a wider door opening means a bigger angle.

Do the ray lengths matter when comparing angles?

No! Ray length has nothing to do with angle size. You can extend or shorten rays without changing the angle. Only the opening between rays determines angle measurement.

What's the difference between acute and obtuse angles?

Acute angles are less than 90° (narrow opening), while obtuse angles are greater than 90° (wide opening). Right angles are exactly 90°.

Can I measure these angles without a protractor?

You can estimate by comparing to a right angle (90°). If an angle looks narrower than a square corner, it's acute. If wider, it's obtuse.

Why does angle B look so much bigger than angle A?

Angle A appears to be around 30-45° (acute), while angle B is approximately 120-135° (obtuse). The difference in their openings makes this comparison clear.

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