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Chapter 3: Q10 (page 81)

Find the values of xand y

Short Answer

Expert verified

Values are x=70and role="math" localid="1637745946360" y=60

Step by step solution

01

Step 1. Label the given figure

02

Step 2. Observations from figure

Arrowheads denotes line segment AB炉is parallel to CD炉

Line segment GC炉is transversal to parallel lines AB炉andCD炉

03

Step 3. Find x degree

鈭�GEAand 鈭�ECDforms a pair of corresponding angles

Postulate 10: If two parallel lines are cut by a transversal then the corresponding angles are congruent

鈭�GEA鈮�鈭�ECD

x=m鈭�ECD

Thus,

04

Step 4. Find y degree

鈭�AEDand 鈭�FEBforms a pair of vertically opposite angles

鈭�AED鈮�鈭�FEB

m鈭�AED=m鈭�FEB

m鈭�AED=50

Since, 鈭�GEA,鈭�AED, and 鈭�DECforms the straight line GC炉so these angles are supplementary angles. That is,

m鈭�GEA+m鈭�AED+m鈭�DEC=180

70+50+y=180

120+y=180

role="math" localid="1637746929112" y=180鈭�120

y=60

Thusy=60

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Most popular questions from this chapter

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

transversal. Use a protractor to measure

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

Classify each pair of angles as alternate interior angles, same-side interior angles, corresponding angles, or none of these.

and

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

State the postulate or theorem that justifies each statement.

m鈭�4+m鈭�6=180

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

Two lines parallel to a third line are parallel to each other
See all solutions

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