Find Angle α in Triangle ABC: Given Angles 27.7° and 41°

Triangle Angle Sum with Decimal Measures

Find the size of angle α \alpha .

27.727.727.7AAABBBCCC41

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:02 Let's find the value of A.
00:05 Remember, the sum of angles in a triangle is always one hundred eighty degrees.
00:10 Now, plug in the known values from the problem, and work towards solving for A.
00:15 Next, gather like terms together.
00:18 Then, make sure to isolate A on one side of the equation.
00:25 And there you have it! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Find the size of angle α \alpha .

27.727.727.7AAABBBCCC41

2

Step-by-step solution

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

Therefore, we can use the formula:

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

Then we will substitute in the known data:

α+27.7+41=180 \alpha+27.7+41=180

α+68.7=180 \alpha+68.7=180

Finally, we will move the variable to the other side while maintaining the appropriate sign:

α=18068.7 \alpha=180-68.7

α=111.3 \alpha=111.3

3

Final Answer

111.3

Key Points to Remember

Essential concepts to master this topic
  • Rule: The sum of all three angles in any triangle equals 180°
  • Technique: Add known angles: 27.7° + 41° = 68.7°, then subtract from 180°
  • Check: Verify 111.3° + 27.7° + 41° = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting that triangle angles always sum to 180°
    Don't just add the given angles together and call it the answer = 68.7° instead of 111.3°! This ignores the fundamental triangle angle sum property. Always remember that all three angles must add up to exactly 180°.

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 do triangle angles always add up to 180°?

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This is a fundamental property of triangles in flat (Euclidean) geometry. It's like a mathematical law - no matter what type of triangle you have, the three interior angles will always sum to exactly 180°!

What if I get a negative answer when subtracting?

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If you get a negative result, check your addition first. Make sure you added the known angles correctly. A triangle angle can never be negative!

Can triangle angles be decimals?

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Absolutely! Angles can be any positive decimal value. Just make sure your final answer, when added to the other two angles, equals exactly 180°.

How precise should my decimal answer be?

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Use the same precision as given in the problem. Here we have 27.7° (one decimal place), so your answer should also have one decimal place for consistency.

What if the sum of two given angles is already 180°?

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That would mean the third angle is 0°, which is impossible in a real triangle. Double-check your problem - there might be an error in the given values.

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