Supplementary angles are those pair of angles who add up to 180°
Two adjacent angles formed by the intersection of two lines are supplementary
Let's analyze each pair of angles given in the question:
• angle KLI and angle KLN
Note these two angles are adjacent and are formed by the crossing of the lines NG and KM. Thus they are supplementary
• angle HIG and angle KLI
These two angles are not supplementary. In fact, they are congruent because they are formed by the crossing of parallel lines with the same line. They are called corresponding angles. This option is not correct
• angle MLI and angle JIG
As the case explained above, those angles are formed when two parallel lines cross with a single line. They are corresponding angles.
• angle HIL and angle KLN
The situation here is identical to the two previous options. The angles are corresponding, or congruent. They have the same measure.
Summarizing, from the options provided, only the second corresponds to a pair of supplementary angles
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