Transversal Angles Math Example 4

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Example 4

hard
Lines mm and nn are cut by a transversal. Corresponding angles are (7x−15)°(7x - 15)° and (4x+27)°(4x + 27)°. Are lines mm and nn parallel? If so, find the angle measure.

Solution

  1. 1
    Step 1: If lines are parallel, corresponding angles are equal. Set them equal to test: 7x−15=4x+277x - 15 = 4x + 27.
  2. 2
    Step 2: Solve: 3x=423x = 42, giving x=14x = 14.
  3. 3
    Step 3: Angle =7(14)−15=98−15=83°= 7(14) - 15 = 98 - 15 = 83°. Check: 4(14)+27=56+27=83°4(14) + 27 = 56 + 27 = 83°. ✓
  4. 4
    Step 4: Since a consistent value of xx makes the angles equal, the lines are parallel.

Answer

Yes, the lines are parallel. Each corresponding angle is 83°83°.
The converse of the Corresponding Angles Theorem: if corresponding angles are equal, the lines are parallel. Setting the expressions equal and solving for xx checks whether a consistent value exists. If it does and makes both expressions equal, the lines must be parallel.

About Transversal Angles

When a transversal (a line that crosses two parallel lines), it creates eight angles with four special relationships: corresponding angles are equal, alternate interior angles are equal, alternate exterior angles are equal, and co-interior (same-side interior) angles are supplementary.

Learn more about Transversal Angles →

More Transversal Angles Examples

Example 1 easy

A transversal crosses two parallel lines. One of the angles formed is [formula]. Find the correspond

Example 2 medium

Two parallel lines are cut by a transversal. Co-interior angles (same-side interior angles) are [for

Example 3 easy

A transversal crosses two parallel lines. An alternate exterior angle is [formula]. What is the meas

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