Question

classify the angle pair ∠mnq and ∠qnp.
options:
nonadjacent and complementary
adjacent and neither complementary nor supplementary
adjacent and complementary
a linear pair

Explanation:

1. Adjacent Check: ∠MNQ and ∠QNP share a common vertex (N) and a common side (NQ), so they are adjacent.
2. Complementary Check: The measure of ∠MNQ is \( 50^\circ \) and ∠QNP is \( 40^\circ \). Their sum is \( 50^\circ + 40^\circ = 90^\circ \), so they are complementary (since complementary angles sum to \( 90^\circ \)).
3. Eliminate Other Options: They are adjacent (so "Nonadjacent" is wrong), their sum is \( 90^\circ \) (not \( 180^\circ \), so "linear pair" is wrong), and they are complementary (so "neither complementary nor supplementary" is wrong). Thus, the correct classification is "Adjacent and complementary".

Answer:

Adjacent and complementary