Triangle Angle Calculation: Finding α When Given 49.6° and 38°

Triangle Angle Sum with Decimal Measures

Find the measure of the angle α \alpha

49.649.649.6AAABBBCCC38

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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
00:10 Collect terms
00:18 Isolate A
00:24 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

49.649.649.6AAABBBCCC38

2

Step-by-step solution

Let's 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:

α+49.6+38=180 \alpha+49.6+38=180

α+87.6=180 \alpha+87.6=180

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

α=18087.6 \alpha=180-87.6

α=92.4 \alpha=92.4

3

Final Answer

92.4

Key Points to Remember

Essential concepts to master this topic
  • Fundamental Rule: Sum of all three angles in any triangle equals 180°
  • Setup Method: Write α + 49.6° + 38° = 180° and solve for α
  • Verification: Check that 92.4° + 49.6° + 38° = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting that ALL three angles must sum to 180°
    Don't just add the two given angles = incomplete calculation! This ignores the third angle and gives meaningless results. Always set up the equation with all three angles equaling 180°.

Practice Quiz

Test your knowledge with interactive questions

True or false:

DE not a side in any of the triangles.
AAABBBCCCDDDEEE

FAQ

Everything you need to know about this question

Why does every triangle have angles that add up to 180°?

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This is a fundamental property of triangles in flat (Euclidean) geometry. No matter what type of triangle - big, small, acute, obtuse - the three interior angles always sum to exactly 180°.

What if I get a negative angle or an angle over 180°?

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Check your arithmetic! In a valid triangle, each angle must be between 0° and 180°. If you get impossible values, you likely made a calculation error.

Do I need to worry about the decimal 49.6°?

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Not at all! Treat decimal angles just like whole numbers. Simply add 49.6 + 38 = 87.6, then subtract from 180°.

How can I double-check my work quickly?

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Add all three angles together: your answer + 49.6° + 38°. If the sum equals exactly 180°, you're correct!

What's the difference between α (alpha) and other angle notations?

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α (alpha) is just a Greek letter used to represent an unknown angle, like using 'x' in algebra. You might also see angles labeled as ∠A, ∠B, or with other Greek letters like β (beta) or θ (theta).

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