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McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
4. Rectangles
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Exercise 28 Page 509

Notice that ∠ 2 and ∠ 3 form alternate interior angles.

m∠ 3=40

Practice makes perfect

Let's analyze the given quadrilateral so that we can find the measure of ∠ 3.

Notice that ∠ 2 and ∠ 3 form 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, by the ∠ 2 and ∠ 3 are congruent and their measures are equal. m ∠ 2=m ∠ 3 We already know that m ∠ 2= 40. Therefore, m ∠ 3= 40 as well.
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