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.