Question

in the diagram to the right, (overline{jl} perp overline{mn}). use the diagram for questions 11-14.

1. classify (angle pkm) and (angle nko).

(check all names that apply.)
☐ adjacent
☐ vertical
☐ complementary
☐ supplementary
☐ linear pair

1. classify (angle nko) and (angle okl).

(check all names that apply.)
☐ adjacent
☐ vertical
☐ complementary
☐ supplementary
☐ linear pair

Explanation:

Question 11: Classify ∠PKM and ∠NKQ

1. Vertical Angles: ∠PKM and ∠NKQ are formed by intersecting lines (MN and PO), so they are vertical angles (opposite angles, equal measure).
2. Supplementary? No, since \( \overline{JL} \perp \overline{MN} \), but vertical angles here don’t sum to \( 180^\circ \) (unless specific conditions, but vertical angles are equal, not necessarily supplementary). Adjacent? No (no common side). Complementary? No (sum to \( 90^\circ \)? Not implied here). Linear Pair? No (not adjacent and forming a line).

1. Adjacent: They share a common side (\( \overline{KQ} \)) and vertex (K).
2. Complementary: Since \( \overline{JL} \perp \overline{MN} \), \( \angle MKL = 90^\circ \), and \( \angle NKQ + \angle QKL = \angle NKL = 90^\circ \) (as \( MN \perp JL \)), so they are complementary.
3. Linear Pair? No (sum to \( 90^\circ \), not \( 180^\circ \)). Vertical? No (not opposite). Supplementary? No (sum to \( 90^\circ \), not \( 180^\circ \)).

Answer:

Vertical

Question 12: Classify ∠NKQ and ∠QKL