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McGraw Hill Integrated II, 2012 View details

5. Angles and Parallel Lines

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Exercise 2 Page 311

What is the relationship between ∠ 5 and ∠ 1? Give a name to each line to help make the diagram more clear to read. Think about what theorem explains the relationship between parallel lines and a transversal. What does it mean for two angles to be congruent?

Angle: m∠ 5=94^(∘)
Theorem: Alternate Exterior Angles Theorem

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It is a given that m∠ 1=94^(∘). Using this information, we need to find the measure of angle ∠ 5. Let's use the given diagram to find these angles.

Next, let's give a name to these lines to further clarify the relationships we are seeking to discover.

These angles are formed by the parallel lines m and n, and the transversal t. They lie on opposite sides of the transversal and on different sides of the parallel lines. According to the definition, these are alternate exterior angles. Therefore, to find the measure of ∠ 5, we can use the Alternate Exterior Angles Theorem.

Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent.

According to the theorem, we can conclude that ∠ 1 and ∠ 5 are congruent and their measures are the same. Therefore, the measure of ∠ 5 is also 94^(∘).

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Exercises p.311-314

Exercise 2 Page 311

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