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x = 6 2/3     The supplementary pair of angle is 78 degree and z = 112degree  = 180 degree  First step is where we can also see z its opposite angle is vertical opposite angle to 112 degree given and label as vertical angle - where we see a line through the 180 degree line at any angle we can call the pair supplementary-   Pairs OR sets of angles an only be called consecutive when they are grouped with a set of parallel line across a straight line and it is only because they add up to 180 they could be either terms so as there isn't parallel shown ; we know we an call a pair of angles upon a straight line supplementary.angles.

Step-by-step explanation:

6 x +38 (+112) = 180 degree as angles on a straight line add up to 180   6 x +38 (+112) = 180    6 x +140 = 180  6 x + 140- 140 = 180-140      6 x  = 40   x = 40/6  x = 6.66666667    x = 6 2/3   Proof  (6( 6 2/3)) + 38 + 112 = 180     = (40+38)+112 = 180 = 78 +112 = 180   Proves the supplementary angle is 78 degree.

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step-by-step explanation: