Parallel Lines Geometry: Calculate Angle α Using 62° and 54° Measurements

Triangle Angle Sum with Parallel Line Properties

Lines a and b are parallel.

What is the size of angle α \alpha ?

aaabbb6254α

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the angle
00:03 Corresponding angles are equal
00:08 Corresponding angles between parallel lines are equal
00:11 The sum of angles in a triangle equals 180
00:14 Therefore we'll sum, equate to 180 and solve for the angle
00:22 Let's isolate the angle
00:32 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Lines a and b are parallel.

What is the size of angle α \alpha ?

aaabbb6254α

2

Step-by-step solution

Please note that according to the definition of corresponding angles, the angle α \alpha corresponds to the angle located on line a and is also within the small triangle created in the drawing.

As we already have one angle in this triangle, we will try to find and calculate the remaining angles.

Furthermore the angle opposite to the angle 62 next to the vertex is also equal to 62 (vertex opposite angles are equal to one other)

Therefore, we can now calculate the missing angle in the small triangle created in the drawing, which is the angle

α \alpha

α=1805462 \alpha=180-54-62

α=64 \alpha=64

3

Final Answer

64

Key Points to Remember

Essential concepts to master this topic
  • Parallel Lines: Corresponding angles are equal when lines are parallel
  • Triangle Sum: All angles in triangle add to 180°: α=1805462=64° \alpha = 180 - 54 - 62 = 64°
  • Check: Verify 54° + 62° + 64° = 180° for triangle angle sum ✓

Common Mistakes

Avoid these frequent errors
  • Confusing angle relationships in parallel line diagrams
    Don't assume α equals 62° just because they look similar = wrong answer of 62°! The angles are related but not equal. Always identify which triangle contains α and use the triangle angle sum property.

Practice Quiz

Test your knowledge with interactive questions

If one of two corresponding angles is a right angle, then the other angle will also be a right angle.

FAQ

Everything you need to know about this question

Why isn't α equal to 62° if the lines are parallel?

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While parallel lines create equal corresponding angles, α isn't corresponding to the 62° angle. The α is part of a different triangle that contains the 54° and 62° angles.

How do I know which angles belong to the same triangle?

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Look for the three vertices that form a closed triangle. In this problem, α, 54°, and 62° all meet at the vertices of one small triangle in the diagram.

What are corresponding angles exactly?

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Corresponding angles are in the same relative position when a line crosses two parallel lines. They're like matching corners - same position, different intersection point.

Can I solve this without using triangle angle sum?

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The triangle angle sum (180° 180° ) is the most direct method here. While other angle relationships exist, this approach gives you α immediately once you identify the correct triangle.

What if I can't see the triangle clearly in the diagram?

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Focus on where the angle labels meet. The 62°, 54°, and α all share vertices that form one complete triangle, even if other lines cross through the area.

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