Triangle Angle Verification: Do 56°, 89°, and 17° Form a Valid Triangle?

Triangle Properties with Angle Sum Verification

Angle A equals 56°.
Angle B equals 89°.
Angle C equals 17°.

Can these angles make a triangle?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:10 Let's find out if these angles make a triangle.
00:13 Remember, the angles in a triangle add up to 180 degrees.
00:18 We'll check if the angles we have add up to 180 degrees.
00:23 First, plug in the angles you know, and add them up.
00:40 If the sum is less than 180, it can't be a triangle.
00:44 Here's how we solve it together. Great job staying with it!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Angle A equals 56°.
Angle B equals 89°.
Angle C equals 17°.

Can these angles make a triangle?

2

Step-by-step solution

We add the three angles to see if they are equal to 180 degrees:

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

The sum of the given angles is not equal to 180, so they cannot form a triangle.

3

Final Answer

No.

Key Points to Remember

Essential concepts to master this topic
  • Rule: Sum of all three angles in any triangle equals 180°
  • Technique: Add given angles: 56° + 89° + 17° = 162°
  • Check: If sum ≠ 180°, then angles cannot form a triangle ✓

Common Mistakes

Avoid these frequent errors
  • Assuming angles can form a triangle without checking the sum
    Don't just look at individual angles and guess they form a triangle = wrong conclusion! Even if each angle looks reasonable, they must add to exactly 180°. Always calculate the sum first: 56° + 89° + 17° = 162° ≠ 180°, so no triangle is possible.

Practice Quiz

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Indicates which angle is greater

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

What if the angles add up to more than 180°?

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Then those angles cannot form a triangle! In our example, 56° + 89° + 17° = 162°, which is less than 180°, so these angles also can't make a triangle.

Can I have negative angles in a triangle?

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No! All angles in a triangle must be positive and less than 180°. Negative angles don't exist in basic triangle geometry.

What's the smallest and largest angle possible in a triangle?

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The smallest angle approaches 0° (but never reaches it), and the largest angle approaches 180° (but never reaches it). Most triangles have angles between these extremes.

How do I check my addition when verifying triangle angles?

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Double-check your arithmetic! For 56° + 89° + 17°:

  • 56 + 89 = 145
  • 145 + 17 = 162
  • Since 162 ≠ 180, no triangle!

Are there any shortcuts to know if angles form a triangle?

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Yes! If you notice that two angles already add up to more than 180°, you don't need to add the third. For example, if two angles are 95° and 90°, that's already 185° > 180°!

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