Co-interior Angles: Identifying α1, β1, α2, β2 with Parallel Lines

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

Corresponding angles are in the same relative position and are equal. Co-interior angles are on the same side of the transversal but at different levels and add up to 180°.

Q: How do I identify which angles are co-interior in this diagram?

Look for angles that are:On the same side of the transversal lineBetween the parallel lines a and bAt different levels (one near line a, one near line b)

Q: Are α1 and β2 co-interior angles?

No! While they're on the same side of a transversal, α1 is above line a and β2 is below line b. Co-interior angles must be between the parallel lines.

Q: What does γ represent in this problem?

The explanation mentions $ \gamma_1 $ and $ \gamma_2 $ as the correct co-interior angles. These would be the angles between lines a and b on the same side of the transversal that sum to 180°.

Co-interior Angles with Transversal Lines

Which angles in the drawing are co-interior given that a is parallel to b?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine which of the angles are acute angles

00:03 Corresponding angles occur on the same side and level of the line

00:19 The sum of the acute angles is 180

00:24 The acute angles occur on the same side of the line

00:29 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which angles in the drawing are co-interior given that a is parallel to b?

Step-by-step solution

Given that line a is parallel to line b, the angles $\alpha_2,\beta_1$ are equal according to the definition of corresponding angles.

Also, the angles $\alpha_1,\gamma_1$ are equal according to the definition of corresponding angles.

Now let's remember the definition of collateral angles:

Collateral angles are actually a pair of angles that can be found on the same side of a line when it crosses a pair of parallel lines.

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

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 angles

γ1+γ2=180

are the collateral angles

Final Answer

$\gamma1,\gamma2$

Key Points to Remember

Essential concepts to master this topic

Definition: Co-interior angles are on same side of transversal
Technique: Find angles between parallel lines: $\gamma_1 + \gamma_2 = 180°$
Check: Co-interior angle pairs always sum to exactly 180 degrees ✓

Common Mistakes

Avoid these frequent errors

Confusing co-interior with corresponding angles
Don't identify angles that are in matching positions as co-interior = wrong angle pairs! Co-interior angles are on the SAME side of the transversal but at different levels. Always look for angles between the parallel lines on one side.

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

Corresponding angles are in the same relative position and are equal. Co-interior angles are on the same side of the transversal but at different levels and add up to 180°.

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

When parallel lines are cut by a transversal, co-interior angles form a linear pair when you imagine them side by side. Since they're supplementary, they must sum to 180°.

How do I identify which angles are co-interior in this diagram?

Look for angles that are:

On the same side of the transversal line
Between the parallel lines a and b
At different levels (one near line a, one near line b)

Are α1 and β2 co-interior angles?

No! While they're on the same side of a transversal, α1 is above line a and β2 is below line b. Co-interior angles must be between the parallel lines.

What does γ represent in this problem?

The explanation mentions $\gamma_1$ and $\gamma_2$ as the correct co-interior angles. These would be the angles between lines a and b on the same side of the transversal that sum to 180°.

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Co-interior Angles: Identifying α1, β1, α2, β2 with Parallel Lines

Co-interior Angles with Transversal Lines

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

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

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

How do I identify which angles are co-interior in this diagram?

Are α1 and β2 co-interior angles?

What does γ represent in this problem?

🌟 Unlock Your Math Potential

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