Find the Alpha Angle in a Triangle with 90° and 100° Angles

Triangle Angle Sum with Impossible Conditions

Find the measure of the angle α \alpha

100100100AAABBBCCC90

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the value of A
00:03 The sum of angles in a triangle equals 180
00:06 Substitute in the relevant values according to the given data and proceed to solve for A
00:12 Isolate A
00:17 A cannot be negative given that it is an angle measure
00:20 Therefore the triangle is invalid and cannot be solved
00:23 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Find the measure of the angle α \alpha

100100100AAABBBCCC90

2

Step-by-step solution

Remember that the sum of angles in a triangle is equal to 180.

Therefore, we will use the formula:

A+B+C=180 A+B+C=180

Let's input the known data:

100+α+90=180 100+\alpha+90=180

190+α=180 190+\alpha=180

α=180190 \alpha=180-190

We should note that it's not possible to get a negative result, and therefore there is no solution.

3

Final Answer

There is no possibility of resolving

Key Points to Remember

Essential concepts to master this topic
  • Rule: Sum of all angles in a triangle equals 180°
  • Technique: Add given angles: 100° + 90° = 190°
  • Check: If sum exceeds 180°, no triangle can exist ✓

Common Mistakes

Avoid these frequent errors
  • Calculating the third angle without checking if triangle is valid
    Don't just solve α = 180° - 190° = -10° and accept negative angles! Negative angles are impossible in triangles. Always check if the given angles can actually form a triangle first.

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 can't angles in a triangle add up to more than 180°?

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This is a fundamental property of triangles in flat geometry. The three interior angles of any triangle must always equal exactly 180°. If they add up to more, it's impossible to form a triangle!

What does it mean when there's no solution?

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It means the problem describes an impossible situation. Just like you can't have a square with 3 sides, you can't have a triangle with angles that sum to more than 180°.

Should I still try to solve for the missing angle?

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Always check first! Add up the known angles before solving. If they already exceed 180°, stop immediately and conclude 'no solution possible'.

Could this be a trick question?

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Not a trick - it's testing your understanding of triangle properties. Recognizing when a problem has no solution is just as important as solving solvable problems!

What if the angles were 100° and 80° instead?

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Then you could solve! 100°+80°+α=180° 100° + 80° + α = 180° gives α=0° α = 0° , which is also impossible. The angles need to be positive and sum to exactly 180°.

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