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Big Ideas Math: Modeling Real Life, Grade 8

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Big Ideas Math: Modeling Real Life, Grade 8 View details

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Exercise 4 Page 134

Use the relationship of angles between parallel lines.

Angle Measure: 133^(∘)
Explanation: See solution.

Let's consider the given diagram.

angles

We know from the diagram that line m is parallel to line n. We also know the measure of one angle, m∠ 2= 47^(∘). To find the measure of ∠ 5, we will use the fact that corresponding angles of parallel lines are congruent. Since ∠ 2 and ∠ 6 are corresponding angles and lines m and n are parallel, these angles are congruent.

angles

Congruent angles have the same measure, so the measure of ∠ 6 is 47^(∘). Finally, note that ∠ 6 and ∠ 5 form a straight line.

angles

Therefore, they are supplementary and the sum of their measures is 180^(∘). With this information, we can finally find the measure of ∠ 5. m∠ 5+ 47^(∘)=180^(∘) ⇕ m∠ 5=133^(∘)

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