Triangle Angle Verification: Can 69°, 93°, and 81° Form a Triangle?

Triangle Angle Sum with Invalid Measurements

Tree angles have the sizes:

69°, 93°, and 81.

Is it possible that these angles are in a triangle?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine whether the following angles can form a triangle
00:03 The sum of angles in a triangle equals 180
00:07 Substitute in the relevant values according to the given data and proceed to solve
00:15 The sum of angles is greater than 180, therefore it cannot be a triangle
00:18 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Tree angles have the sizes:

69°, 93°, and 81.

Is it possible that these angles are in a triangle?

2

Step-by-step solution

Let's remember that the sum of angles in a triangle is equal to 180 degrees.

We'll add the three angles to see if their sum equals 180:

69+81+93=243 69+81+93=243

Therefore, these cannot be the values of angles in any triangle.

3

Final Answer

No.

Key Points to Remember

Essential concepts to master this topic
  • Rule: Sum of all triangle angles must equal exactly 180°
  • Technique: Add given angles: 69° + 93° + 81° = 243°
  • Check: Compare sum to 180°: 243° ≠ 180°, so not a triangle ✓

Common Mistakes

Avoid these frequent errors
  • Assuming angles can form a triangle without checking the sum
    Don't just accept given angles as valid triangle angles = wrong conclusions! This leads to incorrect geometric reasoning and misunderstanding triangle properties. Always verify that the three angles add up to exactly 180° before concluding they can form a triangle.

Practice Quiz

Test your knowledge with interactive questions

True or false:

DE not a side in any of the triangles.
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FAQ

Everything you need to know about this question

Why must triangle angles always add up to 180°?

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This is a fundamental property of triangles in flat (Euclidean) geometry. It's like a mathematical law that never changes - just like how a circle always has 360°!

What if the sum is close to 180° but not exactly?

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Close isn't good enough! The sum must be exactly 180°. If it's 179° or 181°, those angles cannot form a triangle in regular geometry.

Can I have angles larger than 90° in a triangle?

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Yes! You can have one angle larger than 90° (called an obtuse triangle), but the sum of all three must still equal 180°.

How do I quickly check if three angles work?

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  • Add all three angles together
  • Check if the sum equals exactly 180°
  • If yes → valid triangle; if no → not a triangle

What happens if I use these invalid angles anyway?

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You cannot draw a triangle with these angles! In this case, 69°+93°+81°=243° 69° + 93° + 81° = 243° is impossible to construct as a triangle.

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