Find Angle α in a Triangle with Given 50° Angle

Triangle Angle Sum with Isosceles Properties

Find the measure of the angle α \alpha

505050AAABBBCCC50

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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
00:07 Substitute in the relevant values according to the given data and proceed to solve for A
00:10 Group terms
00:15 Isolate A
00:18 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

505050AAABBBCCC50

2

Step-by-step solution

Recall that the sum of angles in a triangle equals 180 degrees.

Therefore, we will use the following formula:

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

Now let's insert the known data:

α+50+50=180 \alpha+50+50=180

α+100=180 \alpha+100=180

We will simplify the expression and keep the appropriate sign:

α=180100 \alpha=180-100

α=80 \alpha=80

3

Final Answer

80

Key Points to Remember

Essential concepts to master this topic
  • Angle Sum Rule: All triangle angles always add up to 180 degrees
  • Technique: Set up equation α+50+50=180 \alpha + 50 + 50 = 180 and solve
  • Check: Verify 80 + 50 + 50 = 180 degrees ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting that two angles are both 50 degrees
    Don't use only one 50° angle in your equation = missing 50 degrees! This gives α=130° \alpha = 130° instead of 80°. Always identify all given angles carefully, especially when a triangle has two equal angles.

Practice Quiz

Test your knowledge with interactive questions

Is DE side in one of the triangles?
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FAQ

Everything you need to know about this question

Why does this triangle have two 50° angles?

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This is an isosceles triangle - it has two equal sides, which means it also has two equal angles. The diagram shows both base angles are 50°.

Can I solve this without the angle sum formula?

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No! The angle sum property (A+B+C=180° A + B + C = 180° ) is the fundamental rule for all triangles. It's the only way to find missing angles when you know the other angles.

What if I got 130° instead of 80°?

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You probably only used one 50° angle instead of both! Remember: α+50+50=180 \alpha + 50 + 50 = 180 , not α+50=180 \alpha + 50 = 180 . Always count all given angles.

How do I know which angle is α?

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Look at the diagram carefully! The angle marked with the Greek letter α (alpha) is at the top vertex of the triangle, opposite to the longest side.

Why can't the answer be 90° or 110°?

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Test it! If α = 90°, then 90 + 50 + 50 = 190°, which is too much for a triangle. If α = 110°, then 110 + 50 + 50 = 210°, which is way too much!

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