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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 36 Page 326

What is the relation between the marked angles? Which theorem relates this pair of angles?

x=9 by the Converse of the Consecutive Interior Angles Theorem

Practice makes perfect

Let's take a look at the given diagram. We can notice that the marked angles are consecutive interior angles.

Since we want lines p and q to be parallel, the given angles need to be supplementary according to the Converse of the Consecutive Interior Angles Theorem. Therefore, the sum of their measures should be equal to 180. (5x+21) + (12x+6) = 180 Now we can solve the equation for x.

(5x+21)+(12x+6)=180

Remove parentheses

5x+21+12x+6=180

Add terms

17x+27=180

LHS-27=RHS-27

17x=153

.LHS /17.=.RHS /17.

x=9

If the value of x is 9, the lines p and q are parallel by the Consecutive Interior Angles Converse.

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