Triangle Angle Sum: Can 56°, 89°, and 17° Form a Valid Triangle?

Triangle Angle Sum with Invalid Combinations

If three angles are sizes 56°, 89°, and 17°.

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 Can these angles potentially form a triangle?
00:03 The sum of the angles in a triangle equals 180
00:07 Insert 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
00:15 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

If three angles are sizes 56°, 89°, and 17°.

Is it possible that these angles are in a triangle?

2

Step-by-step solution

Let's calculate the sum of the angles to see what total we get in this triangle:

56+89+17=162 56+89+17=162

The sum of angles in a triangle is 180 degrees, so this sum is not possible.

3

Final Answer

Impossible.

Key Points to Remember

Essential concepts to master this topic
  • Rule: All triangle angles must sum to exactly 180°
  • Technique: Add given angles: 56° + 89° + 17° = 162°
  • Check: Compare sum to 180°: 162° ≠ 180°, so impossible ✓

Common Mistakes

Avoid these frequent errors
  • Assuming close sums are acceptable
    Don't think 162° is 'close enough' to 180° so the triangle might work = wrong conclusion! In geometry, angle sums must be exact - even 1° off means impossible. Always check if the sum equals exactly 180°.

Practice Quiz

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Is the straight line in the figure the height of the triangle?

FAQ

Everything you need to know about this question

Why must triangle angles add to exactly 180°?

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This is a fundamental law of geometry! Every triangle, no matter its size or shape, has interior angles that sum to exactly 180°. This has been proven mathematically and cannot be violated.

What if my sum is very close to 180°, like 179° or 181°?

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Even being 1 degree off means the triangle is impossible! In mathematics, 'close' isn't good enough - the sum must be exactly 180°.

Could these angles form a different shape instead?

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Yes! These three angles could be part of a quadrilateral (which has angles summing to 360°) or other polygon, but definitely not a triangle.

How do I quickly check if three angles can form a triangle?

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Just add them up! If the sum equals exactly 180°, they can form a triangle. If not, they cannot. It's that simple!

What would happen if I tried to draw this triangle?

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You literally cannot draw it! When you try to close the third angle, you'll find there's either too much or too little space left. The triangle simply won't close properly.

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