Math Teacher Mambo: Angle Pairs - Free Printable

Let’s go step by step through each pair of angles (A to I) and determine:

1. Are they adjacent angles?
→ Adjacent angles must share a common vertex and a common side, but do not overlap.

2. Are they a linear pair?
→ A linear pair is a special kind of adjacent angles — they must be adjacent AND their non-common sides form a straight line (so they add up to 180°).

We’ll analyze each one carefully.

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A.
Angles ∠1 and 2 share the same vertex and one common side. They don’t overlap.
→ So, yes, they are adjacent.
But do their outer rays form a straight line? No — they’re just two small angles next to each other, not forming a straight line.
→ So, not a linear pair.

B.
∠1 and ∠2 share the same vertex, but ∠2 is drawn as an arc that goes around — it looks like ∠2 is the big angle that includes ∠1. That means they overlap.
→ So, not adjacent (because adjacent angles can’t overlap).
Therefore, also not a linear pair.

C.
∠1 and ∠2 share the same vertex and appear to share a common side. They don’t overlap.
→ So, yes, adjacent.
Do their outer rays form a straight line? No — there are other rays in between, and the total isn’t 180°.
→ So, not a linear pair.

D.
∠1 and ∠2 are on opposite sides of a point on a straight line. They share a vertex and a common side (the ray going up), and their other sides form a straight line.
→ So, yes, adjacent.
And since they form a straight line together → yes, linear pair.

E.
∠1 and ∠2 are vertical angles — they are opposite each other when two lines cross. They share a vertex, but no common side.
→ So, not adjacent.
Therefore, not a linear pair.

F.
Same as E — these are vertical angles again. No shared side.
→ Not adjacent, so not a linear pair.

G.
∠1 and ∠2 are completely separate — different vertices, no connection.
→ Not adjacent, so not a linear pair.

H.
∠1 and ∠2 are connected at a point, but they don’t share a common side — they’re kind of “touching” at a corner but not sharing a ray. Also, they look like they’re part of a zigzag, not forming a straight line.
→ Actually, looking closely: they share a vertex, but do they share a side? The diagram shows them meeting at a point, but the sides don’t align to form a continuous ray — so probably not adjacent.
Even if you argue they’re adjacent, their outer sides don’t form a straight line → not a linear pair.
So safest answer: not adjacent (because they don’t clearly share a common side — the figure suggests they’re on different “arms”).

Wait — let me re-examine H. In some interpretations, if two angles meet at a vertex and have a common ray, they’re adjacent. But here, ∠1 is on the left, ∠2 is on the top-right — they might share a vertex but not a side. Actually, in standard geometry diagrams, if they’re drawn like this without a shared ray, they’re not adjacent.
→ So: Not adjacent, therefore not a linear pair.

I.
∠1 and ∠2 share a vertex and a common side. They don’t overlap.
→ So, yes, adjacent.
Do their outer rays form a straight line? No — they’re both acute angles pointing in similar directions.
→ So, not a linear pair.

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Now let’s summarize:

| Pair | Adjacent? | Linear Pair? |
|------|-----------|--------------|
| A | Yes | No |
| B | No (overlap) | No |
| C | Yes | No |
| D | Yes | Yes |
| E | No (vertical) | No |
| F | No (vertical) | No |
| G | No (separate) | No |
| H | No (no common side) | No |
| I | Yes | No |

Final Answer:
A: Adjacent: Yes; Linear Pair: No
B: Adjacent: No (angles overlap); Linear Pair: No
C: Adjacent: Yes; Linear Pair: No
D: Adjacent: Yes; Linear Pair: Yes
E: Adjacent: No (vertical angles, no common side); Linear Pair: No
F: Adjacent: No (vertical angles, no common side); Linear Pair: No
G: Adjacent: No (different vertices); Linear Pair: No
H: Adjacent: No (no common side); Linear Pair: No
I: Adjacent: Yes; Linear Pair: No