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 intersect
- Adjacent (A): Angles that share a common vertex and 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 step by step.

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1.

- Two angles sharing a common vertex and side.
- They are adjacent, but no measure given.
- Not forming a straight line → not linear pair.
- No indication they sum to 90° or 180° → can't confirm C or S.
- Answer: A (Adjacent)

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2.

- Two intersecting lines with two points marked (angles).
- The angles are opposite each other → vertical angles.
- Also, since they're formed by intersecting lines, they are vertical.
- Answer: V (Vertical)

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3.

- Two angles at a vertex, sharing a ray.
- They are adjacent.
- Do they form a straight line? No — not a straight line.
- No degree measures → can't check for C or S.
- Answer: A (Adjacent)

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4.

- Two intersecting lines; two angles marked.
- These angles are opposite → vertical angles.
- Also, they are not adjacent (don’t share a side), so not adjacent.
- But vertical angles are always equal, not necessarily adding to 90° or 180° unless specified.
- Answer: V (Vertical)

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5.

- Right angle shown (90°) with another angle next to it.
- The two angles share a side and vertex → adjacent.
- Together, they make a right angle → complementary (sum = 90°).
- So they are adjacent and complementary.
- Answer: A, C

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6.

- Three rays from a point; two angles marked.
- The two angles share a vertex and a side → adjacent.
- Do they form a straight line? No — not a straight line.
- No degree measures → can’t say if C or S.
- Answer: A (Adjacent)

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7.

- Two angles: 72° and 18°.
- Sum = 72 + 18 = 90° → complementary.
- Are they adjacent? They appear to be separate, not sharing a side → not adjacent.
- But since they are just labeled separately, maybe they’re part of a larger figure?
- However, in the diagram, they are drawn apart — so likely not adjacent, just two angles that happen to add to 90°.
- But the question says "marked angle pair", so if they are both marked and we're to consider them as a pair, and their sum is 90°, then:
- Answer: C (Complementary)

> Note: If they were adjacent and formed a right angle, it would be C and A, but here they are not adjacent.

So only C.

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8.

- Two angles marked at a vertex with three rays.
- They share a vertex and a side → adjacent.
- Do they form a straight line? No — not a straight line.
- No degree measures → can’t determine C or S.
- Answer: A (Adjacent)

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9.

- Two angles marked at a vertex where two lines intersect.
- They are opposite each other → vertical angles.
- So they are vertical.
- Also, they are not adjacent.
- Answer: V (Vertical)

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10.

- Two angles at a vertex, forming a straight line.
- They are adjacent and form a straight line → linear pair.
- Linear pairs are also supplementary (sum to 180°).
- So they are adjacent, supplementary, and linear pair.
- Answer: A, S, LP

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11.

- Two intersecting lines with two angles marked.
- They are opposite each other → vertical angles.
- So V.
- Also, they are not adjacent.
- Answer: V (Vertical)

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12.

- Two angles: 50° and 130°.
- Sum = 50 + 130 = 180° → supplementary.
- Are they adjacent? They don’t appear to share a side or vertex → probably not adjacent.
- But if they are part of a straight line, they might be.
- Looking at the diagram: two separate angles, possibly not connected.
- But since they are labeled together and sum to 180°, we assume they are being compared as a pair.
- Without shared side or vertex, not adjacent.
- But they add to 180°, so supplementary.
- Answer: S (Supplementary)

> Note: Even if not adjacent, if they are just a pair of angles that sum to 180°, they are supplementary.

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✔ Final Answers:

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

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🔍 Explanation Summary:

- Complementary (C): Sum to 90° (e.g., 72° + 18°)
- Supplementary (S): Sum to 180° (e.g., 50° + 130°)
- Vertical (V): Opposite angles from intersecting lines
- Adjacent (A): Share a vertex and side
- Linear Pair (LP): Adjacent and form a straight line → automatically supplementary

Some pairs may have multiple answers (like #5: adjacent and complementary).

Let me know if you'd like this formatted for printing or need the worksheet filled in!