Parallel Lines Proof: Analyzing Angles 2X+10 and 70-X

Parallel Lines with Corresponding Angles

Are lines AB and DC parallel?

2X+102X+102X+1070-X70-X70-XAAABBBCCCDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Are the lines parallel?
00:02 To find out, let's assume they are parallel and try to find X
00:05 Corresponding angles are equal between parallel lines
00:09 Therefore, we'll equate the angles and solve for X
00:15 Let's isolate X
00:20 Since there is a solution for X, the lines are parallel
00:27 Let's substitute the solution we found for X and find the angles
00:39 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Are lines AB and DC parallel?

2X+102X+102X+1070-X70-X70-XAAABBBCCCDDD

2

Step-by-step solution

For the lines to be parallel, the two angles must be equal (according to the definition of corresponding angles).

Let's compare the angles:

2x+10=70x 2x+10=70-x

2x+x=7010 2x+x=70-10

3x=60 3x=60

x=20 x=20

Once we have worked out the variable, we substitute it into both expressions to work out how much each angle is worth.

First, substitute it into the first angle:

2x+10=2×20+10 2x+10=2\times20+10

40+10=50 40+10=50

Then into the other one:

7020=50 70-20=50

We find that the angles are equal and, therefore, the lines are parallel.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Rule: Parallel lines create equal corresponding angles when cut by transversal
  • Technique: Set expressions equal: 2x+10=70x 2x+10 = 70-x then solve
  • Check: Both angles equal 50° when x=20, confirming parallel lines ✓

Common Mistakes

Avoid these frequent errors
  • Assuming lines are parallel without checking angle equality
    Don't just look at the diagram and guess = wrong conclusion! The angles might not actually be equal even if they look similar. Always solve the equation to verify that corresponding angles are truly equal.

Practice Quiz

Test your knowledge with interactive questions

Identify the angle shown in the figure below?

FAQ

Everything you need to know about this question

How do I know which angles to compare for parallel lines?

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Look for corresponding angles - they're in the same relative position when a transversal crosses two lines. In this problem, both angles are on the same side of the transversal and in matching positions.

What if I get different values for the two angles?

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If the angles aren't equal, then the lines are not parallel! Parallel lines always create equal corresponding angles, so unequal angles mean the lines intersect somewhere.

Do I always need to solve for x first?

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Yes! You must find the value of x by setting the expressions equal, then substitute back to find the actual angle measures. This proves whether they're truly equal.

Can I just estimate if the angles look equal?

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Never estimate! Diagrams aren't drawn to scale. You must solve algebraically to get the exact angle measures. In this case, both angles equal exactly 50°.

What other angle relationships prove parallel lines?

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Besides corresponding angles, you can also use:

  • Alternate interior angles (equal)
  • Alternate exterior angles (equal)
  • Co-interior angles (sum to 180°)

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