Find Angle α in a Triangle with 120° and 27° Angles

Triangle Angle Sum with Given Angles

Find the measure of the angle α \alpha

120120120AAABBBCCC27

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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 Collect terms
00:14 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

120120120AAABBBCCC27

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:

120+27+α=180 120+27+\alpha=180

147+α=180 147+\alpha=180

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

α=180147 \alpha=180-147

α=33 \alpha=33

3

Final Answer

33

Key Points to Remember

Essential concepts to master this topic
  • Rule: Sum of all three angles in any triangle equals 180°
  • Technique: Add known angles first: 120° + 27° = 147°
  • Check: Verify sum: 120° + 27° + 33° = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting that triangle angles sum to 180°
    Don't assume angles sum to 90° or 360° like other shapes = wrong answer! Triangles are unique - their interior angles always total exactly 180°. Always use the triangle angle sum theorem: A + B + C = 180°.

Practice Quiz

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Is DE side in one of the triangles?
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FAQ

Everything you need to know about this question

Why do triangle angles always add up to 180°?

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This is the Triangle Angle Sum Theorem - a fundamental property of triangles in flat (Euclidean) geometry. It works for any triangle: acute, obtuse, right, or scalene!

What if I get a negative angle?

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Check your arithmetic! Angles in triangles are always positive. If you get negative, you likely made a calculation error or the given angles don't form a valid triangle.

Can a triangle have two angles bigger than 90°?

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No! If two angles are each greater than 90°, their sum alone would exceed 180°. A triangle can have at most one obtuse angle.

How do I set up the equation?

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Write the angle sum formula: A+B+C=180° A + B + C = 180° . Then substitute the known values and solve for the unknown angle.

What if the angles don't add up to 180°?

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Then the three angles cannot form a triangle! Double-check your given values - there might be an error in the problem or your calculations.

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