Use properties of parallel lines cut by a transversal to find unknown angle measures

Lines that are cut by a transversal may or may not be parallel
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Questions #: 11
Time: 5 minutes
Pass Score: 80.0%
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Corresponding angles property

If two parallel lines are cut by a transversal, each pair of corresponding angles are congruent

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Correct Answer

Explanation

In the figure below

If \(l_1 \parallel l_2\), then

  • ∠ 1 ≅ (1) transparent
  • ∠ 3 ≅ (2) transparent
  • ∠ 2 ≅ (3) transparent
  • ∠ 4 ≅ (4) transparent
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∠ 8
∠ 5
∠ 6
∠ 7
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Correct Answer

Explanation

Alternate interior angles property

If two parallel lines are cut by a transversal, alternate interior angles are congruent

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Correct Answer

Explanation

In the following figure

if \(l_1 \parallel l_2 \) then

  • ∠3 ≅ (1) transparent
  • ∠4 ≅ (2) transparent
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∠6
∠5
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Explanation

Interior angles property

In the figure below, If \(l_1 \parallel l_2\) then

  • ∠3 is supplementary to (1) transparent
  • ∠4 is supplementary to (2) transparent
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∠6
∠5
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Explanation

If a transversal is perpendicular to one of the two parallel lines, it is also perpendicular to the other line

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Explanation

If two lines are parallel to a third line, the are not necessarily parallel to each other

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Explanation

Refer to the below figure

If \(l_1 \parallel l_2 \) and m(∠3) = 120o, find the measures of the other seven angles that are labelled.

  1. m(∠1) =
  2. m(∠2) =
  3. m(∠4) =
  4. m(∠5) =
  5. m(∠6) =
  6. m(∠7) =
  7. m(∠8) =
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Correct Answer

Explanation

Refer to the figure below

transversal_example_1.gif

if \(\overline{AB} \parallel \overline{DE} \), which pairs of angles are congruent?

∠A ≅ ∠1
∠B ≅ ∠2
∠A ≅ ∠3
∠B ≅ ∠4
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Correct Answer

Explanation

In the figure below

\(l_1 \parallel l_2 \).  Find \(x\)

\(x\) =

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Correct Answer

Explanation

In the figure below

\(l_1 \parallel l_2\)

  1. Find \(x\)
  2. Find the measures of both angles labelled in the figure

\(x\) =

m(3x + 20o) =

m(3x - 80o) =

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Correct Answer

Explanation

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