The difference of the same side angles of two parallel lines is 35°. find the measures of these two angles.

Remark

Let the larger angle = x

Let the smaller angle = y

If the angles are unequal but on the same side of the transversal, then they must be supplementary. That's where you get your second equation.

Equations

x + y = 180          Fact about angles and parallel lines.

x - y  = 35           Given

Solution

Add the equations together

2x = 180 + 35       Combine

2x = 215                Divide by 2

2x/2 = 215/2         Divide

x = 107.5

The larger angle is 107.5

The smaller angle is 180 - 107.5 =  72.5

Question: Do they differ by 35?

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