Answer:
- supplementary angles: ∠5 and ∠7
- vertical angles: ∠5 and ∠8
Explanation:
You want to identify a pair of supplementary angles, and a pair of vertical angles in the given figure.
Supplementary angles
Two angles are supplementary if they total 180°. This will be the case for any linear pair of angles. A linear pair of angles combines to form a straight line.
Supplementary angle pairs in the figure are ...
(1, 2), (1, 3), (2, 4), (3, 4), (5, 6), (5, 7), (6, 8), (7, 8)
Vertical angles
Two angles are vertical angles if they are formed by two intersecting lines and if their shared vertex is the point where the lines cross. The angles do not share a side, but have sides formed from opposite rays.
A pair of crossing lines forms two sets of vertical angles.
Vertical angle pairs in the figure are ...
(1, 4), (2, 3), (5, 8), (6, 7)
Your answer will be a pair of angles from the first list, and a pair of angles from the second list. The highlighted pairs are the ones we list at the top of the answer.
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Additional comment
Angles may be supplementary in a variety of other contexts. Adjacent angles in a parallelogram are supplementary, as are opposite angles in a quadrilateral inscribed in a circle. When parallel lines are crossed by a transversal, consecutive interior angles are supplementary, as are consecutive exterior angles. (There are no parallel lines in the given figure for this problem.)