Question

identify the relationship between $\angle hgi$ and $\angle igj$ as completely as possible.
options:
adjacent and complementary
adjacent and supplementary
vertical
adjacent

Explanation:

1. Adjacency Check: ∠HGI and ∠IGJ share the common vertex G and the common side GI, with their non-common sides (GH and GJ) forming a straight line. This makes them adjacent angles.
2. Supplementary Check: Angles that form a straight line sum to 180 degrees. Since GH and GJ are collinear, ∠HGI + ∠IGJ = 180°, so they are supplementary.
3. Eliminate Other Options: They are not complementary (sum is not 90°), not vertical (vertical angles are opposite each other, not adjacent), and "Adjacent" alone is not the complete relationship.

Answer:

Adjacent and Supplementary