First create a pair of angles that are vertical but not supplementary. Can you create another pair of angles that are vertical and also supplements?
Sometimes
Practice makes perfect
Let's begin by creating two angles that are vertical but not supplements of each other.
∠ WMS and ∠ NME are vertical angles because their sides form a pair of opposite rays, but they are not supplementary angles. We know that because both angles are acute, and the sum of the measures of two acute angles is less than 180^(∘). Let's now create a situation where two vertical angles are also supplements of each other.
Looking at the diagram, we can see that ∠ WMS and ∠ NME are vertical and also supplementary angles.
m∠ WMS+m∠ NME=90^(∘)+90^(∘)=180^(∘)
We can conclude that vertical angles are sometimes supplements of each other.
