Triangle Angle Analysis: Can 30°, 60°, and 90° Form a Valid Triangle?

Q: What happens if the angles don't add up to 180°?

If three angles don't sum to 180 degrees, they cannot form a triangle! The triangle would be impossible to draw in flat geometry.

Q: Is this a special type of triangle?

Yes! A triangle with angles 30°, 60°, and 90° is called a 30-60-90 right triangle. It's one of the most important special triangles in geometry.

Q: Can I have more than one 90° angle in a triangle?

No! If you had two 90° angles, that's already 180°. There would be no room for a third angle, making it impossible.

Q: What if I get exactly 180° but one angle is negative?

Triangle angles must be positive numbers between 0° and 180°. Negative angles don't exist in triangles, even if the sum works out.

Q: Do I always need to check this rule?

Yes! The Triangle Angle Sum Theorem is fundamental. Whether you're given three angles or calculating them, always verify they add to 180°.

Triangle Angle Sum with Special Triangles

Angle A is equal to 30°.
Angle B is equal to 60°.
Angle C is equal to 90°.

Can these angles form a triangle?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's see if these angles make a triangle.

00:12 Remember, all triangle angles add up to 180 degrees.

00:17 Let's add the given angles and check if they total 180.

00:22 Plug in the values and calculate step by step.

00:39 Great! The angles add up to 180 degrees, so it is a triangle.

00:57 And that's how you determine if angles form a triangle!

Step-by-step written solution

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Understand the problem

Angle A is equal to 30°.
Angle B is equal to 60°.
Angle C is equal to 90°.

Can these angles form a triangle?

Step-by-step solution

We must first add the three angles to see if they equal 180 degrees:

$30+60+90=180$

The sum of the angles equals 180, therefore they can form a triangle.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Rule: All triangle angles must sum to exactly 180 degrees
Technique: Add angles: 30° + 60° + 90° = 180°
Check: Sum equals 180°, so these angles form a valid triangle ✓

Common Mistakes

Avoid these frequent errors

Forgetting to check if angles sum to 180°
Don't just accept any three angles as a triangle = invalid shapes! Without checking the sum, you might think 45°, 50°, and 100° form a triangle (they equal 195°). Always verify that the three angles add up to exactly 180 degrees.

Practice Quiz

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Indicates which angle is greater

FAQ

Everything you need to know about this question

What happens if the angles don't add up to 180°?

If three angles don't sum to 180 degrees, they cannot form a triangle! The triangle would be impossible to draw in flat geometry.

Is this a special type of triangle?

Yes! A triangle with angles 30°, 60°, and 90° is called a 30-60-90 right triangle. It's one of the most important special triangles in geometry.

Can I have more than one 90° angle in a triangle?

No! If you had two 90° angles, that's already 180°. There would be no room for a third angle, making it impossible.

What if I get exactly 180° but one angle is negative?

Triangle angles must be positive numbers between 0° and 180°. Negative angles don't exist in triangles, even if the sum works out.

Do I always need to check this rule?

Yes! The Triangle Angle Sum Theorem is fundamental. Whether you're given three angles or calculating them, always verify they add to 180°.

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