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Find the values of xand y

Short Answer

Expert verified

Values arex=10andy=45

Step by step solution

01

Step 1. Label the given figure

02

Step 2. Observations from figure

Arrowheads denotes line segment ABยฏis parallel to DCยฏ

Line segments BCยฏand ADยฏare transversal to these parallel lines

03

Step 3. Find x degree

โˆ BADand โˆ ADCforms 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.

mโˆ BAD+mโˆ ADC=1804x+14x=18018x=180x=18018

Thus,x=10

04

Step 4. Find y degree

โˆ DCBand โˆ CBAforms 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.

mโˆ DCB+mโˆ CBA=1802y+90=180

2y=180โˆ’90y=902

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