Identifying Pairs of Angles worksheet with diagrams and questions.

Explanation:
We are asked to identify each pair of indicated angles as adjacent, vertical, or linear.

Let’s recall what each term means:

- Adjacent angles: Two angles that share a common vertex and a common side, but do not overlap. They are next to each other.
- Vertical angles: Angles opposite each other when two lines cross. They share a vertex but no sides; they are formed by intersecting lines and are always equal.
- Linear angles (also called a linear pair): Two adjacent angles whose non-common sides form a straight line — meaning they add up to 180°. So they are adjacent *and* supplementary.

Now go through each diagram one by one:

1) Diagram 1: Two angles share a vertex and a side (ray PB), and their outer rays (PA and PC) form a straight line. So they are adjacent and also form a straight line → this is a linear pair.
✔ Answer: linear

2) Diagram 2: Two lines intersect at point P. Angles labeled x and y are opposite each other (not sharing a side). That makes them vertical angles.
✔ Answer: vertical

3) Diagram 3: Two angles share vertex P and a side (the upward ray), but their outer rays do *not* form a straight line (they form a “corner” shape, like an L). So they are just adjacent.
✔ Answer: adjacent

4) Diagram 4: Two angles share vertex P and a side (the horizontal ray), and the outer rays go straight up and straight down — forming a straight vertical line. So they are adjacent and make 180° → linear.
✔ Answer: linear

5) Diagram 5: Angles share vertex P and a side (the slanted ray), but the outer rays are not in a straight line — it's a bent shape (like a “V” with an extra arm). So just adjacent.
✔ Answer: adjacent

6) Diagram 6: Two lines cross at point P. Angles x and y are opposite each other → vertical.
✔ Answer: vertical

7) Diagram 7: Angles share vertex P and a side (the left horizontal ray), and the outer rays go right and down — not forming a straight line. So just adjacent.
✔ Answer: adjacent

8) Diagram 8: Two lines intersect at P. Angles x and y are opposite → vertical.
✔ Answer: vertical

Let me double-check all:

1. Linear ✔
2. Vertical ✔
3. Adjacent ✔
4. Linear ✔
5. Adjacent ✔
6. Vertical ✔
7. Adjacent ✔
8. Vertical ✔

All match definitions.

Final Answer:
1) linear
2) vertical
3) adjacent
4) linear
5) adjacent
6) vertical
7) adjacent
8) vertical