Find Alpha in an 80° Triangle: Geometric Angle Measurement

Triangle Angle Sum with Known Measurements

Find the measure of the angle α \alpha

808080AAABBBCCC55

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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
00:11 Group the terms
00:14 Isolate A
00:19 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

808080AAABBBCCC55

2

Step-by-step solution

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

Therefore, we will use the following formula:

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

Now let's input the known data:

80+55+α=180 80+55+\alpha=180

135+α=180 135+\alpha=180

We'll move the term to the other side and keep the appropriate sign:

α=180135 \alpha=180-135

α=45 \alpha=45

3

Final Answer

45

Key Points to Remember

Essential concepts to master this topic
  • Triangle Rule: Sum of all three angles always equals 180 degrees
  • Technique: Add known angles: 80° + 55° = 135°, then subtract
  • Check: Verify 80° + 55° + 45° = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting the 180-degree rule
    Don't just guess angle measures or assume they follow patterns = wrong answers! Students often forget that ALL triangles have angles totaling exactly 180°. Always use the formula A + B + C = 180° and solve algebraically.

Practice Quiz

Test your knowledge with interactive questions

Is DE side in one of the triangles?
AAABBBCCCDDDEEE

FAQ

Everything you need to know about this question

Why do all triangles have angles that add to 180°?

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This is a fundamental property of triangles in flat (Euclidean) geometry. No matter the size or shape of the triangle, the three interior angles will always sum to exactly 180 degrees!

What if I can't see all the angle measurements clearly?

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Look for angle markings like the curved lines in the diagram. The numbers 80° and 55° are clearly labeled, so you have everything needed to find the third angle!

Can the missing angle be negative?

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No! All angles in a triangle must be positive and less than 180°. If you get a negative answer, check your arithmetic - you likely made an error.

How do I set up the equation correctly?

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Use the format: A+B+C=180° A + B + C = 180° . Substitute known values: 80°+55°+α=180° 80° + 55° + \alpha = 180° , then solve for the unknown angle.

What if my answer doesn't match the choices?

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Double-check your addition and subtraction. Common errors include: 80 + 55 = 135, then 180 - 135 = 45. Make sure each step is correct!

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