The parallel postulate states that if the measures of the consecutive interior angles of two lines add up to a number other than 180, the lines aren't parallel. Since the lines in the figure are, we know that the consecutive angles must be supplementary to each other. We can set up an algebraic equation to represent this. j + 35 + 2k + 5 = 180 Now, we can simplify as much as we can. j + 2k + 40 = 180 j + 2k = 140 Uh oh. We're stuck. Let's back up and look at the picture again. Since the adjacent angles 2k + 5 and 62° make a straight angle, we can set up another equation that sets the sum of these two to 180°. 2k + 5 + 62 = 180 Now, we can solve for k. 2k + 67 = 180 2k = 113 k = 56.5 Substituting that into the other equation, we can solve for j. j + 2k = 140 j + 2(56.5) = 140 j + 113 = 140 j = 27 It's always a good idea to double-check your work. We can do this by using other characteristics of parallel lines (like congruent corresponding angles). j + 35 ≟ 62 27 + 35 ≟ 62 62 = 62 |