Supplementary angles are a pair of angles that sum to 180^(∘).
Complementary angles are a pair of angles that sum to 90^(∘).
Vertical angles are a pair of angles where the sides form opposite rays.
Let's sketch an intersection of roads and label the different angles we can see.
Next, we will identify the different kinds of angles in this sketch.
Supplementary Angles
In our diagram we have three pairs of supplementary angles. We can identify two sets of linear pairs and another pair of right angles. Remember, the only requirement for supplementary angles is that they sum to 180^(∘). To simplify our drawing, we will replace the roads with rays.
We have the following supplementary angles.
Linear Pair: &∠ D and ∠ E
Linear Pair: &∠ A and ∠ E
Right Angles: &∠ A and ∠ D
Complementary Angles
The only angles that are not 90^(∘) are ∠ B and ∠ C. However, if we put them together they make a right angle.
Therefore, ∠ B and ∠ C are complementary angles.
Vertical Angles
Examining the diagram, we can identify two pairs of opposite rays.
