Exercise 41 Page 590

Let's analyze the given figure.

Note that since the segments formed on the right part of the diagram are congruent, we can solve the equation 10-2x = 12-3x to find x.

10-2x = 12-3x

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Solve for x

AddEqn

LHS+3x=RHS+3x

10+x=12

SubEqn

LHS-10=RHS-10

x=2

To find y we can use the Congruent Parts of Parallel Lines Corollary. Since we are given three parallel lines that cut one transversal into congruent segments, they cut every transversal into congruent segments.

Now we can solve the equation y+ 45 = 2y- 115 to find y. Let's do it!

y+4/5 = 2y-11/5

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Solve for y

SubEqn

LHS-y=RHS-y

4/5=y-11/5

AddEqn

LHS+11/5=RHS+11/5

4/5+11/5=y

AddFrac

Add fractions

15/5=y

CalcQuot

Calculate quotient

3=y

RearrangeEqn

Rearrange equation

y=3

We found that x=2 and y=3.