Triangle Angle Validation: Do 31°, 122°, and 85° Form a Valid Triangle?

Triangle Angle Sum with Invalid Measures

Tree angles have the sizes:

31°, 122°, and 85.

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 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
00:11 The sum of angles is greater than 180, therefore they cannot form a triangle
00:17 This is the solution

Step-by-step written solution

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1

Understand the problem

Tree angles have the sizes:

31°, 122°, and 85.

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:

31+122+85=238 31+122+85=238

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 triangle angles must equal exactly 180°
  • Technique: Add given angles: 31° + 122° + 85° = 238°
  • Check: If sum ≠ 180°, angles cannot form triangle ✓

Common Mistakes

Avoid these frequent errors
  • Assuming angles can form a triangle without checking
    Don't skip adding the angles and assume they form a valid triangle = wrong conclusion! Large angles like 122° should signal potential issues. Always calculate the sum first and verify it equals exactly 180°.

Practice Quiz

Test your knowledge with interactive questions

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 property of triangles in flat geometry! No matter what type of triangle - big, small, acute, or obtuse - the three interior angles always sum to 180°.

What if my sum is close to 180° but not exact?

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In math problems, the sum must be exactly 180°. In real measurements, small differences might be due to rounding, but for theoretical problems, anything other than 180° means no triangle exists.

Can a triangle have an angle bigger than 90°?

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Yes! Obtuse triangles have one angle greater than 90°. But since all three angles must still sum to 180°, the other two angles must be quite small to compensate.

How do I spot that angles won't work before calculating?

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Look for warning signs: If you see an angle close to or over 120°, be suspicious! Also, if two angles already add up to more than 120°, the third would need to be negative.

What's the largest possible angle in a triangle?

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Just under 180°! As one angle approaches 180°, the other two must approach 0°, making the triangle extremely flat. In practice, angles are usually much smaller.

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