Special Angle Pairs Notes - Lindsay Bowden - Free Printable

Let's solve each of the 12 problems on this "Special Angle Pairs Practice" worksheet. The goal is to identify each marked angle pair as:

- Complementary (C): Two angles that add up to 90°
- Supplementary (S): Two angles that add up to 180°
- Vertical (V): Angles opposite each other when two lines cross
- Adjacent (A): Angles that share a vertex and a side but do not overlap
- Linear Pair (LP): Adjacent angles that form a straight line (i.e., supplementary and adjacent)

We’ll go through each one carefully.

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1.

Two angles sharing a common vertex and side, forming a "corner" shape with three rays.

- They share a vertex and a side, so they are adjacent (A).
- They don't form a straight line or right angle, so not necessarily C or S.
- Not vertical (not opposite).
- Answer: A

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2.

Two intersecting lines, with two dots marking angles across from each other.

- These angles are opposite each other at the intersection → vertical angles.
- Vertical angles are always equal, but not necessarily complementary or supplementary unless specified.
- So: V

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3.

Two angles formed by two rays from a common vertex, one above the other.

- They share a vertex and a side, so adjacent (A).
- They don’t appear to form a straight line or right angle.
- Answer: A

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4.

Two intersecting lines, with two angles marked — one in each opposite corner.

- These are opposite angles → vertical angles → V
- Also, if you look closely, they might be part of a linear pair with others, but these two are vertical.
- Answer: V

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5.

Right angle formed by two perpendicular lines, and another ray making an acute angle inside it.

- One angle is 90° (right angle), and the other is smaller.
- The two angles shown (one being the right angle, the other part of it) are adjacent and together make 90°.
- So they are complementary (C) and adjacent (A).
- But are they linear pair? No — not a straight line.
- Are they supplementary? No — sum is 90°, not 180°.
- Answer: C, A

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6.

Three rays from a common point, with two angles marked near the center.

- The two angles share a vertex and a side → adjacent (A)
- They don’t form a straight line, so not LP.
- Not vertical (not opposite).
- Do they add to 90° or 180°? Not obvious — no measures given.
- So only A

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7.

Two angles labeled: 72° and 18°.

- 72 + 18 = 90° → complementary (C)
- Are they adjacent? Yes — they appear to be next to each other forming a right angle.
- So also adjacent (A)
- Answer: C, A

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8.

Multiple rays from a point, two angles marked near the center.

- They share a vertex and a side → adjacent (A)
- Do they form a straight line? No.
- Are they vertical? No — not opposite.
- Sum? Unknown → can't say C or S.
- Answer: A

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9.

Two angles marked on a straight line — one on top, one below.

- They share a vertex and a side.
- Together they form a straight line → linear pair (LP)
- Therefore, they are supplementary (S) and adjacent (A)
- Answer: S, A, LP

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10.

Two angles at a vertex, forming a straight line.

- They are adjacent and form a straight line → linear pair (LP)
- So they are supplementary (S) and adjacent (A)
- Answer: S, A, LP

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11.

Two intersecting lines, with two angles marked — one in each opposite corner.

- These are vertical angles → V
- Also, each has a supplementary adjacent angle, but these two are opposite → V
- Answer: V

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12.

Two angles: 50° and 130°

- 50 + 130 = 180° → supplementary (S)
- Are they adjacent? They are separate, not sharing a side → not adjacent
- Not vertical (not opposite)
- Not linear pair (don’t form a straight line together)
- So just S

> Note: Even though they are not adjacent, they are still supplementary because their measures add to 180°.

- Answer: S

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✔ Final Answers:

| # | Answer |
|---|--------|
| 1 | A |
| 2 | V |
| 3 | A |
| 4 | V |
| 5 | C, A |
| 6 | A |
| 7 | C, A |
| 8 | A |
| 9 | S, A, LP |
|10 | S, A, LP |
|11 | V |
|12 | S |

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🔍 Summary of Key Concepts:

- Complementary (C): Sum = 90°
- Supplementary (S): Sum = 180°
- Vertical (V): Opposite angles from intersecting lines
- Adjacent (A): Share a vertex and side
- Linear Pair (LP): Adjacent angles forming a straight line → always supplementary

Some pairs may have multiple labels (e.g., both adjacent and supplementary).

Let me know if you'd like this formatted for printing or want explanations drawn on the diagram!