Opposite angles formed by an intersection of two lines.
Now, let's consider the given diagram.
To determine a pair of adjacent angles, let's take a look at the given diagram, looking for a pair of angles that share a vertex and a common side.
Looking at the diagram, ∠ LJK and ∠ KJQ share J as a vertex and JK as a side. Therefore, these angles are adjacent. Now, let's look for a pair of angles whose measures sum to 90^(∘) — a pair of complementary angles.
Looking at the markings on the given diagram, ∠ MJP is a right angle — its measure is 90^(∘). As ∠ MJN and ∠ NJP are adjacent angles that sum to ∠ MJP, they are complementary. Now, let's look for a pair of angles that sum to 180^(∘) — a pair of supplementary angles.
Looking at the markings on the given diagram, ∠ LJK and ∠ KJP sum to the straight angle ∠ LJP. Therefore, the sum of the measures of these angles is the measure of ∠ LJP — 180^(∘). As a result, ∠ LJK and ∠ KJP are supplementary. Finally, let's look for a pair of vertical angles. These angles are on the opposite sides of an intersection of two lines.
Looking at the diagram, ∠ LJK and ∠ PJN are on the opposite sides of an intersection of LP and NK. Therefore, these angles are vertical.
