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Chapter 3: Q11 (page 81)

Find the values of xand y

Short Answer

Expert verified

Values are x=14 andy=9

Step by step solution

01

Step 1. Label the given figure

02

Step 2. Observations from figure

Arrowheads denote line segment AB炉is parallel to XY炉

Line segments YB炉,XB炉,andXA炉are transversal to the parallel lines

03

Step 3. Find x degree

鈭�YXBand 鈭�XBAforms a pair of alternate interior angles

Theorem 3-2: If two parallel lines are cut by a transversal then the alternate interior angles are congruent.

鈭�XBA鈮�鈭�YXBm鈭�XBA=m鈭�ECD3x=42x=423x=14

Thus,x=14

04

Step 4. Find y degree

90+6y鈭�6+3x=180鈭�XYB and 鈭�YBAforms a pair of same-side interior angles

Theorem 3-3: If two parallel lines are cut by a transversal then the same-side interior angles are supplementary.

m鈭�XYB+m鈭�YBA=180

90+6y鈭�6+3x=180

84+6y+3脳14=180

6y=180鈭�84鈭�42

y=546

y=9

Thusy=9

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Most popular questions from this chapter

Name the two lines and the transversal that form each pair of angles.

and

Use two lines of notebook paper as parallel lines and draw any

transversal. Use a protractor to measure

Measure one pair of same side interior angles. Repeat the experiment with another transversal. What appears to be true?

If m鈭�1=xwhat are the measures of the other numbered angels?

Name the two lines and the transversal that form each pair of angles.

and

Complete each statement with the word always, sometimes, or never.

Two planes parallel to the same plane are ?parallel to each other.
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