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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

Chapter Test

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Exercise 17 Page 211

Use theConverse of the Alternate Exterior Angles Theorem.

x=5

Practice makes perfect

Both of the given angles are on the inner part of the potential parallel lines, and are on opposite sides of the transversal. Therefore, the angles can be classified as alternate interior angles. According to the Converse of the Alternate Exterior Angles Theorem, if the angles are congruent, the lines are parallel.

If these angles are congruent, then the lines will be parallel. Recall that two congruent angles have the same measure. 14x-5 = 13x Let's solve this equation.

14x-5 = 13x

LHS-13x=RHS-13x

x-5=0

LHS+5=RHS+5

x=5

The angles are congruent for x=5. Therefore, for this value of x, we have that l ∥ m.