Classify Angle ABC: Identifying an Angle Less Than 90 Degrees

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

An acute angle is less than $ 90^\circ $ (sharp and narrow), while an obtuse angle is greater than $ 90^\circ $ but less than $ 180^\circ $ (wide and open).

Q: How can I remember which angle is which?

Think of acute as 'a-cute' (small and sharp) for angles less than $ 90^\circ $. Obtuse sounds like 'obtuse person' (slow/dull) for wider, bigger angles!

Q: Can an angle be exactly 90 degrees and still be acute?

No! An angle that measures exactly $ 90^\circ $ is called a right angle, not acute. Acute means strictly less than $ 90^\circ $.

Q: Why does the diagram show an arc near point B?

The small arc marks the angle being measured. It shows you exactly which angle to focus on - in this case, the angle formed by rays BA and BC meeting at vertex B.

Q: What if I can't tell from the picture if it's less than 90 degrees?

Always rely on the given information in the problem, not just the visual! The problem states the angle is less than $ 90^\circ $, so use that fact to classify it.

Angle Classification with Degree Measurements

$∢\text{ABC}$ is an angle measuring less than 90°.

What kind of angle angle is it?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$∢\text{ABC}$ is an angle measuring less than 90°.

What kind of angle angle is it?

Step-by-step solution

To determine what kind of angle $\angle \text{ABC}$ is, let's examine the given information: the angle is less than $90^\circ$ .

Step 1: Recall the types of angles based on their measurements:

An acute angle measures less than $90^\circ$ .
A right angle measures exactly $90^\circ$ .
An obtuse angle measures greater than $90^\circ$ but less than $180^\circ$ .
A flat angle measures exactly $180^\circ$ .

Step 2: Match the given information with these definitions.

Since $\angle \text{ABC}$ measures less than $90^\circ$ , it fits the definition of an acute angle.

Therefore, the angle $\angle \text{ABC}$ is an acute angle.

Final Answer

Acute angle

Key Points to Remember

Essential concepts to master this topic

Rule: Acute angles measure less than $90^\circ$
Technique: Compare given angle measurement to $90^\circ$ benchmark
Check: If angle < $90^\circ$ , it's acute; verify with diagram ✓

Common Mistakes

Avoid these frequent errors

Confusing angle types based on visual appearance
Don't guess angle type just by looking at a diagram = wrong classification! Drawings can be misleading and not to scale. Always use the actual degree measurement given in the problem to determine the angle type.

Practice Quiz

Test your knowledge with interactive questions

a is parallel to b.

Calculate the angles shown in the diagram.

FAQ

Everything you need to know about this question

What's the difference between acute and obtuse angles?

An acute angle is less than $90^\circ$ (sharp and narrow), while an obtuse angle is greater than $90^\circ$ but less than $180^\circ$ (wide and open).

How can I remember which angle is which?

Think of acute as 'a-cute' (small and sharp) for angles less than $90^\circ$ . Obtuse sounds like 'obtuse person' (slow/dull) for wider, bigger angles!

Can an angle be exactly 90 degrees and still be acute?

No! An angle that measures exactly $90^\circ$ is called a right angle, not acute. Acute means strictly less than $90^\circ$ .

Why does the diagram show an arc near point B?

The small arc marks the angle being measured. It shows you exactly which angle to focus on - in this case, the angle formed by rays BA and BC meeting at vertex B.

What if I can't tell from the picture if it's less than 90 degrees?

Always rely on the given information in the problem, not just the visual! The problem states the angle is less than $90^\circ$ , so use that fact to classify it.

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Classify Angle ABC: Identifying an Angle Less Than 90 Degrees

Angle Classification with Degree Measurements

❤️ Continue Your Math Journey!

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

What's the difference between acute and obtuse angles?

How can I remember which angle is which?

Can an angle be exactly 90 degrees and still be acute?

Why does the diagram show an arc near point B?

What if I can't tell from the picture if it's less than 90 degrees?

🌟 Unlock Your Math Potential

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