Classify Angle ABC: Analyzing a 67° and 25° Geometric Construction

Q: How do I remember the difference between acute and obtuse angles?

Think of it this way: Acute sounds like 'a-cute' - small and sharp, less than 90°. Obtuse sounds like 'obvious' - big and obvious, greater than 90°!

Q: Why does the triangle sum property always work?

This is a fundamental rule of geometry! No matter what shape or size triangle you have, the three interior angles will always add up to exactly $ 180^\circ $.

Q: What if I calculated 92° instead of 88°?

Check your arithmetic! $ 25^\circ + 67^\circ = 92^\circ $, so $ 180^\circ - 92^\circ = 88^\circ $. A common mistake is adding incorrectly or forgetting to subtract from 180°.

Q: Can angle ABC ever be exactly 90°?

Yes! If the other two angles added up to exactly 90°, then angle ABC would be a right angle. But since $ 25^\circ + 67^\circ = 92^\circ $, we get $ 88^\circ $ instead.

Q: Is there a quick way to check my angle classification?

Absolutely! Once you calculate the angle: Less than 90° = AcuteExactly 90° = RightGreater than 90° = Obtuse

Angle Classification with Triangle Sum Property

According to the data in the diagram, what type of angle is angle ABC?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's figure out what type of angle A B C is.

00:08 Remember, the whole angle equals the sum of its parts.

00:13 Look at the angle. It seems bigger than 90 degrees.

00:17 So, this angle is called an obtuse angle because it's more than 90 degrees.

00:23 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

According to the data in the diagram, what type of angle is angle ABC?

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Gather the known angles in the triangle.
Step 2: Use the angle sum property of the triangle to find the unknown angle.
Step 3: Identify the type of angle based on the angle measure.

Let's calculate:
Given angles are $25^\circ$ and $67^\circ$ .
Step 1: Calculate $\angle ABC$ using the angle sum property:
$\angle ABC = 180^\circ - (25^\circ + 67^\circ) = 180^\circ - 92^\circ = 88^\circ$ .
Since $\angle ABC = 88^\circ$ , it is an obtuse angle.
An obtuse angle is any angle larger than $90^\circ$ and less than $180^\circ$ .

Therefore, the type of angle ABC is Obtuse.

Final Answer

Obtuse

Key Points to Remember

Essential concepts to master this topic

Triangle Sum Rule: All interior angles always add to exactly 180°
Calculation Method: Unknown angle = 180° - (25° + 67°) = 88°
Classification Check: Since 88° < 90°, angle ABC is acute ✓

Common Mistakes

Avoid these frequent errors

Misclassifying 88° as obtuse
Don't think 88° is obtuse just because it's close to 90° = wrong classification! An obtuse angle must be greater than 90°. Always remember: acute angles are less than 90°, right angles equal 90°, and obtuse angles are greater than 90°.

Practice Quiz

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Is DE side in one of the triangles?

FAQ

Everything you need to know about this question

How do I remember the difference between acute and obtuse angles?

Think of it this way: Acute sounds like 'a-cute' - small and sharp, less than 90°. Obtuse sounds like 'obvious' - big and obvious, greater than 90°!

Why does the triangle sum property always work?

This is a fundamental rule of geometry! No matter what shape or size triangle you have, the three interior angles will always add up to exactly $180^\circ$ .

What if I calculated 92° instead of 88°?

Check your arithmetic! $25^\circ + 67^\circ = 92^\circ$ , so $180^\circ - 92^\circ = 88^\circ$ . A common mistake is adding incorrectly or forgetting to subtract from 180°.

Can angle ABC ever be exactly 90°?

Yes! If the other two angles added up to exactly 90°, then angle ABC would be a right angle. But since $25^\circ + 67^\circ = 92^\circ$ , we get $88^\circ$ instead.

Is there a quick way to check my angle classification?

Absolutely! Once you calculate the angle:

Less than 90° = Acute
Exactly 90° = Right
Greater than 90° = Obtuse

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