Co-interior Angles: Identifying α, β, γ, δ Between Parallel Lines

Co-interior Angles with Transversal Identification

Lines a and b are parallel.

Which of the following angles are co-interior?

αααβββγγγδδδaaabbb

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Step-by-step video solution

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00:00 Which angles are unilateral?
00:03 The lines are parallel according to the given data
00:06 Unilateral angles are located on the same side of the line
00:13 Unilateral angles sum to 180
00:16 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Lines a and b are parallel.

Which of the following angles are co-interior?

αααβββγγγδδδaaabbb

2

Step-by-step solution

Let's remember the definition of consecutive angles:

Consecutive angles are, in fact, a pair of angles that can be found on the same side of a straight line when this line crosses a pair of parallel straight lines.

These angles are on opposite levels with respect to the parallel line to which they belong.

The sum of a pair of angles on one side is one hundred eighty degrees.

Therefore, since line a is parallel to line b and according to the previous definition: the anglesβ+γ=180 \beta+\gamma=180

are consecutive.

3

Final Answer

β,γ \beta,\gamma

Key Points to Remember

Essential concepts to master this topic
  • Definition: Co-interior angles are on same side between parallel lines
  • Technique: Find angles between parallels, like β and γ in diagram
  • Check: Co-interior angles always sum to 180° when lines are parallel ✓

Common Mistakes

Avoid these frequent errors
  • Confusing co-interior with alternate angles
    Don't pick angles on opposite sides of the transversal = wrong angle pairs! This misses the key property that co-interior means 'same side'. Always identify angles that are both between the parallel lines AND on the same side of the transversal.

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

What does 'co-interior' actually mean?

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Co-interior means together inside! These angles are on the same side of the transversal (the line crossing the parallels) and between the two parallel lines.

How do I tell which angles are on the same side?

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Draw an imaginary line along the transversal. Angles on the left side are together, and angles on the right side are together. In this diagram, β and γ are both on the right side of the transversal.

Why do co-interior angles add up to 180°?

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When parallel lines are cut by a transversal, co-interior angles are supplementary. This happens because alternate interior angles are equal, and adjacent angles on a straight line sum to 180°.

Are α and δ co-interior angles?

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No! While α and δ are both between the parallel lines, they're on opposite sides of the transversal. Co-interior angles must be on the same side.

What's the difference between co-interior and corresponding angles?

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Corresponding angles are in the same relative position but one is above line a and one is above line b. Co-interior angles are both between the parallel lines on the same side.

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