Calculate X: Corresponding Angles with Parallel Lines and 20° Measurement

Q: How do I know these are alternate angles and not corresponding angles?

Alternate angles are on opposite sides of the transversal and between the parallel lines, forming a 'Z' pattern. Corresponding angles are on the same side in matching positions, forming an 'F' pattern.

Q: Why do I set 2x equal to 20?

Because alternate angles are equal when formed by parallel lines! The angle marked 20° and the angle marked 2x are alternate angles, so they must have the same measure.

Q: What if I got x = 20 instead of x = 10?

You likely set x = 20 instead of 2x = 20. Remember to look carefully at what the variable represents - here it's 2x, not just x!

Q: How can I remember the different angle relationships?

Alternate angles: Make a 'Z' shape, always equalCorresponding angles: Make an 'F' shape, always equalCo-interior angles: On same side, add up to 180°

Q: Do I always divide by the coefficient of x?

Yes! Whatever number is multiplied by x, you need to divide both sides by that number to isolate x. Here, since we have 2x, we divide both sides by 2.

Alternate Angles with Algebraic Expressions

The angles below are formed between two parallel lines.

Calculate the value of X.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:05 Parallel lines according to the given data

00:15 Alternate angles are equal between parallel lines

00:20 Isolate X

00:30 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The angles below are formed between two parallel lines.

Calculate the value of X.

Step-by-step solution

Since the angle equal to 20 and the angle 2x are alternate angles, they are equal to each other.

Therefore:

$2x=20$

We divide both sections by 2:

$\frac{2x}{2}=\frac{20}{2}$

$x=10$

Final Answer

$10$

Key Points to Remember

Essential concepts to master this topic

Rule: Alternate angles formed by parallel lines are always equal
Technique: Set up equation: $2x = 20$ then divide both sides by 2
Check: Substitute x = 10: $2(10) = 20$ matches given angle ✓

Common Mistakes

Avoid these frequent errors

Confusing alternate angles with other angle relationships
Don't assume angles are vertical or corresponding when they're actually alternate = wrong setup! This leads to incorrect equations like x = 20 instead of 2x = 20. Always identify the angle relationship first by checking their positions relative to the parallel lines and 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 know these are alternate angles and not corresponding angles?

Alternate angles are on opposite sides of the transversal and between the parallel lines, forming a 'Z' pattern. Corresponding angles are on the same side in matching positions, forming an 'F' pattern.

Why do I set 2x equal to 20?

Because alternate angles are equal when formed by parallel lines! The angle marked 20° and the angle marked 2x are alternate angles, so they must have the same measure.

What if I got x = 20 instead of x = 10?

You likely set x = 20 instead of 2x = 20. Remember to look carefully at what the variable represents - here it's 2x, not just x!

How can I remember the different angle relationships?

Alternate angles: Make a 'Z' shape, always equal
Corresponding angles: Make an 'F' shape, always equal
Co-interior angles: On same side, add up to 180°

Do I always divide by the coefficient of x?

Yes! Whatever number is multiplied by x, you need to divide both sides by that number to isolate x. Here, since we have 2x, we divide both sides by 2.

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