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

Can a triangle have a right angle?

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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