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Core Connections Integrated II, 2015 View details

2. Section 3.2

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Exercise 86 Page 184

What is the relationship between angles in a linear pair?

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From the diagram we can identify a few angle relationships.

Let's start by analyzing the consecutive interior angles. For each of these angle pairs the two lines cut by the third line are parallel, which means they are supplementary angles by the Consecutive Interior Angles Theorem.

(2x-1^(∘))+3x&=180^(∘) 3x+y&=180^(∘) Therefore, A and D are both correct. Next, we we will take a look at the alternate interior angles. Again, since the two lines cut by the third line are parallel, we know they are congruent according to the Alternate Interior Angles Theorem. 2x-1^(∘)=5y-10^(∘) This means C is correct as well. The last equation, B, implies that a linear pair is congruent. This is not true, as the angles of a linear pair are supplementary. 2x-1^(∘)+(4^(∘)-x)=180^(∘) Therefore, B is incorrect.