Triangle Angle Validation: Can 50°, 41°, and 81° Form a Triangle?

Triangle Angle Sum with Invalid Measurements

Tree angles have the sizes:

50°, 41°, and 81.

Is it possible that these angles are in a triangle?


❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine whether the following angles could 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
00:10 The sum of angles is less than 180, therefore it cannot be a triangle
00:13 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:

50°, 41°, 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:

50+41+81=172 50+41+81=172

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

3

Final Answer

Impossible.

Key Points to Remember

Essential concepts to master this topic
  • Rule: Sum of all angles in any triangle equals exactly 180°
  • Technique: Add given angles: 50° + 41° + 81° = 172°
  • Check: Compare sum to 180°: if not equal, impossible triangle ✓

Common Mistakes

Avoid these frequent errors
  • Assuming close sums are acceptable
    Don't think 172° is 'close enough' to 180° = wrong conclusion! Even 1° difference means impossible triangle geometry. Always require exact 180° sum for valid triangles.

Practice Quiz

Test your knowledge with interactive questions

Determine the size of angle ABC?

DBC = 100°

DDDBBBCCCAAA10040

FAQ

Everything you need to know about this question

Why must triangle angles add up to exactly 180°?

+

This is a fundamental property of triangles in flat geometry! It's proven mathematically and never changes - no exceptions allowed.

What if I get 179° or 181°? Is that close enough?

+

No! Triangle angle sums must be exactly 180°. Any other sum means the three angles cannot form a triangle, period.

Could there be a calculation error in the problem?

+

Always double-check your addition: 50+41+81=172 50 + 41 + 81 = 172 . If you get 172° (not 180°), the angles are definitely invalid for triangles.

Are there any triangles where angles don't add to 180°?

+

In regular flat geometry, no. However, in advanced curved geometry (like on spheres), angle sums can differ - but that's beyond basic triangle rules!

How can I remember this triangle rule?

+

Think: 'Triangle = 180'. The word 'triangle' has 8 letters, and 1-8-0 reminds you of the angle sum!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Angles questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations