Name two angles adjacent with 5

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In geometry, two angles are adjacent if they have a common side and a common vertex. In other words, adjacent angles are directly next to each other and do not overlap.

Adjacent Angles Sample Questions

Adjacent Angles Examples:

In our first example, ∠a is adjacent to ∠b. They share a common vertex, which is the corner point A. They also share a common side, line AD. ∠a and ∠b are adjoined by line AD, but they do not overlap.

In our second example, we see ∠1, ∠2, and ∠3. We see that ∠1 and ∠2 are adjacent because they have a common vertex and a common side. We see the same thing with ∠2 and ∠3, which also share a vertex and one side. Let’s consider ∠1 and ∠3. Although they share a vertex, they are not adjacent because they do not have a common side.

What are adjacent angles?

Based on our definition and the above examples, we can conclude that all pairs of adjacent angles share two properties: (1) a common vertex and (2) a common side. If they are missing one of these components, then they are not adjacent. We can classify pairs of angles as adjacent or not adjacent by looking for these two properties. 

There are many special relationships between pairs of angles. Identifying adjacent angles will help you recognize other angle relationships, such as supplementary and complementary angles.

Adjacent Angles Sample Questions

Here are a few sample questions going over adjacent angles.

Question #1:

Which of the following statements is true?

∠1 and ∠2 are not adjacent

Question #2:

Which angles are adjacent?

Question #3:

Which angles are not adjacent?

Question #4:

Juan is studying leaf veins and notices adjacent angles in the plant structure. He draws the diagram below and records four pairs of adjacent angles. One of Juan’s adjacent angle pairs is incorrect. Based on the diagram, which pair of angles is not adjacent?

Question #5:

Keisha and James are looking at a map of city streets and notice a lot of adjacent angles. James draws the image shown to illustrate the angles they find. Keisha points out that ∠AOE and ∠COD are adjacent because they share a vertex and one side. James disagrees. He says that these angles do not have a common side. Who is correct, and why?

James is correct because both angles share the same vertex but they do not have a common side.

Keisha is correct because both angles share the vertex O and line AD.

James is incorrect because ∠AOE and ∠COD do not have the same vertex.

Keisha is incorrect because there is no ∠AOE shown on the map.

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