Pre-Algebra worksheet on angle relationships with diagrams illustrating complementary, supplementary, vertical, adjacent, alternate interior, corresponding, and alternate exterior angles.

Let's solve each problem step by step, identifying the angle relationships based on the diagrams.

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Part 1: Name the relationship: complementary, supplementary, vertical, or adjacent.

#### 1)
- Two lines intersect, forming angles `a` and `b`.
- Angles `a` and `b` are next to each other and form a straight line (linear pair).
- A linear pair adds up to 180° → Supplementary.

✔ Answer: Supplementary

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#### 2)
- Angles `a` and `b` share a common vertex and side, but they don’t form a straight line.
- They are not opposite, nor do they add to 90° or 180° visibly.
- They are next to each other with a common side and vertex → Adjacent.

✔ Answer: Adjacent

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#### 3)
- Two lines cross, forming four angles.
- Angles `a` and `b` are directly opposite each other at the intersection.
- These are vertical angles.

✔ Answer: Vertical

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#### 4)
- Angles `a` and `b` are at the same vertex, sharing a side.
- There’s a right angle symbol between them → they form a right angle together.
- So, `a + b = 90°` → Complementary.

✔ Answer: Complementary

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#### 5)
- Angles `a` and `b` are next to each other and share a common side and vertex.
- They form a right angle together (indicated by the square corner).
- So, `a + b = 90°` → Complementary.

✔ Answer: Complementary

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#### 6)
- Angles `a` and `b` share a vertex and a side.
- They are next to each other, forming part of a larger angle.
- But no indication of 90° or 180°.
- They are adjacent.

✔ Answer: Adjacent

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Part 2: Name the relationship: alternate interior, corresponding, or alternate exterior.

These involve parallel lines cut by a transversal.

We assume the lines are parallel unless otherwise indicated.

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#### 7)
- Two parallel lines crossed by a transversal.
- Angle `a` is on the top right, angle `b` is on the bottom left.
- They are on opposite sides of the transversal and between the two lines.
- That makes them Alternate Interior angles.

✔ Answer: Alternate Interior

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#### 8)
- Parallel lines, transversal.
- Angle `a` is on the top right, angle `b` is on the top left.
- Both are on the same side of the transversal, and both are above the lines.
- They are in the same relative position → Corresponding.

✔ Answer: Corresponding

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#### 9)
- Two parallel lines crossed by a transversal.
- Angle `a` is on the top right, angle `b` is on the bottom left.
- They are on opposite sides of the transversal.
- Both are outside the two lines → Alternate Exterior.

✔ Answer: Alternate Exterior

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#### 10)
- Two horizontal parallel lines, one diagonal transversal.
- Angle `a` is above the top line, on the right side.
- Angle `b` is below the bottom line, on the right side.
- They are on the same side of the transversal and in the same relative position (both on the right).
- So, they are Corresponding angles.

✔ Answer: Corresponding

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✔ Final Answers:

1) Supplementary
2) Adjacent
3) Vertical
4) Complementary
5) Complementary
6) Adjacent
7) Alternate Interior
8) Corresponding
9) Alternate Exterior
10) Corresponding

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🔍 Explanation Summary:

- Complementary: Two angles that add to 90°.
- Supplementary: Two angles that add to 180°.
- Vertical: Opposite angles formed by two intersecting lines.
- Adjacent: Share a common side and vertex, but do not overlap.
- Alternate Interior: Inside the parallel lines, on opposite sides of the transversal.
- Alternate Exterior: Outside the parallel lines, on opposite sides of the transversal.
- Corresponding: Same relative position at each intersection (e.g., top-right, bottom-left).

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