Triangle Angles Analysis: Multiple Obtuse Angles Possibility

Triangle Angle Properties with Multiple Obtuse Constraints

Can a triangle have more than one obtuse angle?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine whether a triangle can have more than one obtuse angle
00:03 According to the drawing, we can observe that it's impossible and needs another side
00:06 Now the triangle would become a quadrilateral, therefore it's impossible
00:09 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Can a triangle have more than one obtuse angle?

2

Step-by-step solution

If we try to draw two obtuse angles and connect them to form a triangle (i.e: only 3 sides), we will see that it is not possible.

Therefore, the answer is no.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Rule: Sum of all triangle angles always equals 180°
  • Technique: One obtuse angle (>90°) leaves <180° for remaining two angles
  • Check: If two angles >90°, their sum >180° which exceeds triangle limit ✓

Common Mistakes

Avoid these frequent errors
  • Assuming multiple obtuse angles are possible without checking angle sum
    Don't just think about drawing two obtuse angles = impossible triangle! Two angles over 90° each means their sum exceeds 180°, leaving no room for a third angle. Always verify that angle combinations satisfy the 180° rule.

Practice Quiz

Test your knowledge with interactive questions

Look at the angles shown in the figure below.

What is their relationship?

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FAQ

Everything you need to know about this question

What exactly is an obtuse angle?

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An obtuse angle is any angle greater than 90° but less than 180°. Think of it as 'wider' than a right angle (90°).

Why can't a triangle have two obtuse angles?

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Because the angles in any triangle must add up to exactly 180°. If you have two obtuse angles (each >90°), their sum alone would exceed 180°, leaving no room for a third positive angle!

Can a triangle have exactly one obtuse angle?

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Yes! A triangle can have one obtuse angle. The other two angles must be acute (less than 90°) to make the total equal 180°. This is called an obtuse triangle.

What's the largest possible obtuse angle in a triangle?

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The largest obtuse angle approaches 180° but can never reach it. As the obtuse angle gets larger, the other two angles get smaller and approach 0°.

How do I remember this rule?

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Think of it this way: 180° total budget for all three angles. If you 'spend' more than 90° twice, you've already exceeded your budget before adding the third angle!

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