Find Angle α in Triangle ABC: Given 94° Angle Measurement

Triangle Angle Sum with Impossible Configurations

Find the measure of the angle α \alpha

949494AAABBBCCC92

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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 the angles in a triangle equals 180
00:06 Insert the relevant values according to the data and proceed to solve for A
00:09 Collect terms
00:14 Isolate A
00:17 A is an angle measure and must be positive, therefore it's impossible
00:20 This is the solution

Step-by-step written solution

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1

Understand the problem

Find the measure of the angle α \alpha

949494AAABBBCCC92

2

Step-by-step solution

It is known that the sum of angles in a triangle is 180 degrees.

Since we are given two angles, we can calculate a a

94+92=186 94+92=186

We should note that the sum of the two given angles is greater than 180 degrees.

Therefore, there is no solution possible.

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 any triangle equals 180°
  • Technique: Add given angles: 94° + 92° = 186°
  • Check: If sum exceeds 180°, no triangle can exist ✓

Common Mistakes

Avoid these frequent errors
  • Calculating the third angle without checking feasibility
    Don't subtract from 180° when given angles sum to more than 180° = nonsensical negative angle! This violates the fundamental triangle angle sum property. Always verify that given angles sum to less than 180° before attempting to find the third angle.

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 I just subtract 186° from 180°?

+

Because that gives you -6°, which is impossible! Angles in a triangle must be positive and their sum must equal exactly 180°.

What does it mean when there's no solution?

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It means the given measurements cannot form a real triangle. In geometry, some problems have no solution when the given information violates mathematical rules.

How do I know when a triangle is impossible?

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Check if the sum of any two given angles exceeds 180°. If it does, no triangle can exist with those angle measurements.

Could there be a mistake in the problem?

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Sometimes! But in this case, the problem is testing whether you recognize an impossible triangle. The correct answer is that no triangle can be formed.

Are there other ways a triangle can be impossible?

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Yes! In addition to angle sums exceeding 180°, triangles are impossible when:

  • Any angle is 0° or negative
  • Any angle is 180° or greater
  • Side lengths violate the triangle inequality

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