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McGraw Hill Integrated II, 2012 View details

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Exercise 25 Page 326

What is the relationship between ∠ 1 and ∠ 5?

Angle: m∠ 5=123
Theorem: Alternate Exterior Angles Theorem

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It is given that m∠ 1=123. Using this information, we need to find the measure of angle 5. Let's find these angles on the given diagram.

These angles are formed by two parallel lines and the transversal. 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. To find the measure of ∠ 5, we can use 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 this theorem, ∠ 1 and ∠ 5 are congruent and their measures are the same. Therefore, the measure of ∠ 5 is also 123.

Subchapter links

1 Postulates and Paragraph Proofs p.324

2 Algebraic Proof p.324

3 Proving Segment Relationships p.325

4 Proving Angle Relationships p.325

5 Angle and Parallel Lines p.326

6 Proving Lines Parallel p.326

Exercise 25 Page 326

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