Finding Angle α: Using 83° and 29° in Parallel Lines

Parallel Lines with Transversal Angle Relationships

a,b,c parallel to one another

Find a α \alpha

aaabbbccc8329α

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Step-by-step video solution

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00:05 Let's find the angle together.
00:11 Remember, corresponding angles are equal when lines are parallel.
00:21 We have a pair of corresponding angles here.
00:27 Adjacent angles add up to 180 degrees.
00:32 So, let's add them up, set it equal to 180, and find the angle.
00:41 Now, we isolate the angle to solve it.
00:50 And that's how we solve this problem!

Step-by-step written solution

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1

Understand the problem

a,b,c parallel to one another

Find a α \alpha

aaabbbccc8329α

3

Final Answer

68

Key Points to Remember

Essential concepts to master this topic
  • Rule: Corresponding angles are equal when lines are parallel
  • Technique: Use alternate interior angles: 83° and 29° sum to find third angle
  • Check: Triangle angle sum equals 180°: 83° + 29° + 68° = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Confusing angle relationships in parallel lines
    Don't assume α equals 83° or 29° directly = ignores triangle properties! These are separate angles that help find α through triangle angle relationships. Always identify which angles form a triangle and use the 180° sum rule.

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 can't α just equal 83° since they look like corresponding angles?

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Corresponding angles are equal, but α isn't directly corresponding to the 83° angle. You need to use the triangle that contains α, where the angles must sum to 180°.

How do I identify which angles are in the same triangle as α?

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Look for the enclosed triangle that contains α as one of its vertices. The three angles of this triangle - including α - must add up to 180°.

What if I get confused about which angle relationships to use?

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Start by identifying parallel line relationships to find known angles, then focus on the triangle containing α. Use triangle angle sum as your final step.

Can I solve this problem without using parallel line properties?

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No! The parallel lines give you the angle measurements needed. Without parallel line relationships like corresponding or alternate interior angles, you wouldn't know the triangle's other angles.

How do I check if 68° is correct?

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Add all three angles in the triangle: if they equal 180°, your answer is right! Also verify that you correctly identified parallel line angle relationships.

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