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Glencoe Math: Course 3, Volume 2

GM

Glencoe Math: Course 3, Volume 2 View details

Mid-Chapter Check

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Exercise 4 Page 408

Use the relationship of vertical angles between lines that intersect.

57^(∘)

Practice makes perfect

Let's consider the given diagram.

angles

To find the measure of ∠ 2, we will first use the fact that when two lines intersect, vertical angles are formed on opposite sides of the point of intersection, and these angles are always congruent.

angles

Congruent angles have the same measure, so the measure of ∠ 1 is 80^(∘).

angles

Now, note that ∠ 2 and the angles with measures 80^(∘) and 43^(∘) form a straight line.

angles

Therefore, the sum of their measures is 180^(∘). With this information, we can finally find the measure of ∠ 2. m∠ 2+43^(∘)+80^(∘)=180^(∘) ⇕ m∠ 2=57^(∘)

Subchapter links

Vocabulary Check p.408

Skills Check and Problem Solving p.408