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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

7. Vectors

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Exercise 65 Page 690

Notice that ∠ 1 and ∠ 5 are alternate interior angles.

30

Practice makes perfect

Let's analyze the given quadrilateral so that we can find the measure of ∠ 5.

Firstly, notice that ∠ 1 and ∠ 5 are alternate interior angles. Because our quadrilateral is a rectangle, both pairs of opposite sides are parallel. Recall the following theorem.

Alternate Interior Angles Theorem
If parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Therefore, ∠ 1 and ∠ 5 are congruent. We are also given that the measure of ∠ 1 is 30. m ∠ 5=m ∠ 1 ⇔ m ∠ 5 = 30

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Exercises p.687-690