Solve for X: Parallel Lines with Angles (50+X) and (70-X)

Q: How do I know these are alternate interior angles?

Look at the diagram! The angles are on opposite sides of the transversal (diagonal line) and between the parallel lines. This makes them alternate interior angles, which are always equal.

Q: What if I got X = -10 instead?

Check your algebra! You should get $ 50 + X = 70 - X $, which gives $ 2X = 20 $, so $ X = 10 $. Negative values often mean you made a sign error.

Q: Why can't these angles be corresponding angles?

Corresponding angles are in the same position relative to each intersection. These angles are in different positions - one is above-right, the other is below-left of their intersection points.

Q: What if the lines weren't parallel?

If lines aren't parallel, alternate interior angles are not equal! The parallel line condition is crucial - it's what makes these angles have the same measure.

Alternate Interior Angles with Variable Expressions

Calculate X given that the lines in the diagram below are parallel.

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Step-by-step video solution

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00:00 Calculate X

00:03 Parallel lines according to the given data

00:07 Alternate angles are equal between parallel lines

00:13 Arrange the equation and isolate X

00:26 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Calculate X given that the lines in the diagram below are parallel.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Property: Alternate interior angles are equal when lines are parallel
Technique: Set expressions equal: (50 + X) = (70 - X)
Check: Substitute X = 10: both angles equal 60° ✓

Common Mistakes

Avoid these frequent errors

Setting angles as supplementary instead of equal
Don't add the angles to get 180° = wrong relationship! Alternate interior angles are equal, not supplementary. Always identify the angle relationship first before setting up your equation.

Practice Quiz

Test your knowledge with interactive questions

Does the drawing show an adjacent angle?

FAQ

Everything you need to know about this question

How do I know these are alternate interior angles?

Look at the diagram! The angles are on opposite sides of the transversal (diagonal line) and between the parallel lines. This makes them alternate interior angles, which are always equal.

What if I got X = -10 instead?

Check your algebra! You should get $50 + X = 70 - X$ , which gives $2X = 20$ , so $X = 10$ . Negative values often mean you made a sign error.

Why can't these angles be corresponding angles?

Corresponding angles are in the same position relative to each intersection. These angles are in different positions - one is above-right, the other is below-left of their intersection points.

Do I need to find the actual angle measures?

Not always! The question asks for X, but it's good practice to find the angles: both equal $50 + 10 = 60°$ and $70 - 10 = 60°$ .

What if the lines weren't parallel?

If lines aren't parallel, alternate interior angles are not equal! The parallel line condition is crucial - it's what makes these angles have the same measure.

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