Question

what is the relationship between ∠1 and ∠2?
a. vertical and complementary
b. complementary and adjacent
c. supplementary and adjacent
d. supplementary and vertical

Explanation:

To determine the relationship between ∠1 and ∠2, we analyze their properties:

1. Adjacent Angles: ∠1 and ∠2 share a common side and vertex, so they are adjacent.
2. Supplementary Angles: ∠1 and ∠2 form a linear pair (they lie on a straight line), so their sum is \( 180^\circ \), meaning they are supplementary.

Now, evaluate the options:

• Option A: Vertical angles are opposite each other (∠1 and ∠3 are vertical), so A is incorrect.
• Option B: Complementary angles sum to \( 90^\circ \), but ∠1 + ∠2 = \( 180^\circ \), so B is incorrect.
• Option C: ∠1 and ∠2 are adjacent (share a side/vertex) and supplementary (sum to \( 180^\circ \)), so C matches.
• Option D: Vertical angles are not adjacent, so D is incorrect.

Answer:

C. supplementary and adjacent