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5.What is the measurement of <1 that makes line a parallel to line b?5x+630+ 2x)

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Weare asked to find which measurement of angle "1" will make the lines a and b parallel in the following image:

So, if we want the lines a and b to be parallel, then the alternate internal angles labeled 5 x + 6 and 30 + 2 x must be EQUAL. That is:

5 x + 6 = 30 + 2 x

solving for "x", we proceed to subtract 2 x from both sides:

5 x - 2 x + 6 = 30

3 x + 6 = 30

subtract 6 from both sides:

3 x = 30 - 6

3 x = 24

divide both sides by 3:

x = 24 / 3 =

x = 8

Then, if x = 8 degrees, then the supplementary angle to angle <1 is:

30 + 2 x = 30 + 2 (8) = 30 + 16 = 46 degrees

Then angle <1 is 180 degrees minus 46 degrees, that is:

<1 = 180 - 46 = 134 degrees.

<1 measures 134 degrees.

5.What is the measurement of <1 that makes line a parallel to line b?5x+630+ 2x-example-1
User OttherCreek
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