Calculate α + B: Geometric Angle Addition with Parallel Lines

Q: How do I identify which angles are alternate?

Alternate angles are on opposite sides of the transversal (the line cutting through the parallels) and at different levels. They form a 'Z' pattern when you connect them!

Q: What if the diagram showed different angle measures?

The relationship stays the same! Alternate angles are always equal, and angles on a straight line always sum to 180°. Only the specific numbers would change.

Q: How can I remember the difference between alternate and corresponding angles?

Alternate: 'Z' pattern, opposite sides of transversalCorresponding: 'F' pattern, same side of transversalBoth types are equal when lines are parallel!

Q: What does the shaded region in the diagram represent?

The shaded regions help visualize the angles being measured. They show exactly which angles α and β refer to, making it easier to identify their relationship.

Angle Relationships with Parallel Line Intersections

Calculate the expression

$\alpha+B$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate B + A

00:06 Alternate angles are equal between parallel lines

00:24 Let's substitute appropriate values in the sum and solve

00:34 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Calculate the expression

$\alpha+B$

Step-by-step solution

According to the definition of alternate angles:

Alternate angles are angles located on two different sides of the line that intersects two parallels, and that are also not on the same level with respect to the parallel to which they are adjacent.

It can be said that:

$\alpha=30$

$\beta=150$

And therefore:

$30+150=180$

Final Answer

$180$

Key Points to Remember

Essential concepts to master this topic

Alternate Angles: Angles on opposite sides of transversal are equal
Technique: Identify $\alpha = 30°$ and $\beta = 150°$ using parallel line properties
Check: Sum equals 180° since angles are supplementary on straight line ✓

Common Mistakes

Avoid these frequent errors

Confusing alternate angles with corresponding angles
Don't assume α = 150° just because it's near the 150° mark = wrong sum of 300°! This confuses alternate angles (equal) with adjacent angles (supplementary). Always identify which angles are actually alternate by their position on opposite sides 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

How do I identify which angles are alternate?

Alternate angles are on opposite sides of the transversal (the line cutting through the parallels) and at different levels. They form a 'Z' pattern when you connect them!

Why does α + β = 180° in this problem?

While α and β are alternate angles individually, in this diagram they happen to be supplementary because they lie on a straight line. $30° + 150° = 180°$

What if the diagram showed different angle measures?

The relationship stays the same! Alternate angles are always equal, and angles on a straight line always sum to 180°. Only the specific numbers would change.

How can I remember the difference between alternate and corresponding angles?

Alternate: 'Z' pattern, opposite sides of transversal
Corresponding: 'F' pattern, same side of transversal

Both types are equal when lines are parallel!

What does the shaded region in the diagram represent?

The shaded regions help visualize the angles being measured. They show exactly which angles α and β refer to, making it easier to identify their relationship.

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