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Find the values of x and y that make the lines shown in red parallel.

Short Answer

Expert verified

The value that represent x is 50°and the value that represent y is 20°.

Step by step solution

01

Step 1. Determine the equation that represents the equation of x

Mark the segments of the provided figure.

According to the transversal AB the provided parallel lines consist of angles that are having the same measurement which are DABand ABCso,

DAB=ABC

Substitute the value of these angles and isolate the variable x.

5y°=2x°x°=5y°2

02

Step 2. Determine the equation that represents the difference of x and y

According to the transversal EC the provided parallel lines consist of angles that are having the same measurement which are EADand ACBso,

EAD=ACB

Substitute the value of these angles.

30°=xy°

xy°=30°

03

Step 3. By using the obtained equations determine the value of x and y

Substitute the value of x from x°=5y°2into the equation xy°=30° and determine the value of y.

5y2y=305y2y2=30

3y=60

y=603

=20°

Substitute the value of y into the equation x°=5y°2and determine the value of x.

role="math" localid="1637920472360" x=520°2=50°

04

Step 4. Make the conclusion

The obtained value of x is 50° and y is 20°.

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