Vertically Opposite Angles: Foundation (Year 6) | CGP Plus - Free Printable

Let's solve each of the problems on the worksheet step by step, using the properties of vertically opposite angles and angles on a straight line.

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🔷 Key Concepts:

1. Vertically Opposite Angles are equal.
2. Angles on a straight line add up to 180°.
3. Angles around a point add up to 360°.
4. A right angle is 90°.

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✔ Problem 1:

> Diagram: Two lines intersect. One angle is marked as 130°, and angles labeled `a` and `b`.

- The angle opposite to 130° is also 130° → so a = 130° (vertically opposite).
- The angle adjacent to 130° forms a straight line → so it’s 180° - 130° = 50°.
- The angle b is vertically opposite to this 50° → so b = 50°.

✔ Answer:
a = 130°, b = 50°

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✔ Problem 2:

> Diagram: Two lines intersect. One angle is 100°, and two angles labeled `a`.

- The angle adjacent to 100° is 180° - 100° = 80° (straight line).
- The angle `a` is vertically opposite to that 80° → so a = 80°.

✔ Answer:
a = 80°

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✔ Problem 3:

> Diagram: Two lines intersect. One angle is 100°, and two angles labeled `a` and `b`. Given: angle a is 20° more than angle b.

- The angle opposite to 100° is also 100° (vertically opposite).
- So the remaining two angles (`a` and `b`) must be adjacent to 100° and form straight lines.
- Since angles on a straight line sum to 180°:
- The angle adjacent to 100° is 180° - 100° = 80°.
- So `a + b = 80°`, because they are on a straight line together.
- Also given: a = b + 20°

Now solve:
- Substitute into the equation:
- $ a + b = 80 $
- $ (b + 20) + b = 80 $
- $ 2b + 20 = 80 $
- $ 2b = 60 $
- $ b = 30 $
- $ a = 30 + 20 = 50 $

✔ Answer:
a = 50°, b = 30°

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✔ Problem 4:

> Diagram: Two lines intersect. One angle has a right angle (90°) symbol, and two angles labeled `a`.

- The right angle means one angle is 90°.
- The angle vertically opposite to it is also 90°.
- The other two angles must be equal and sum to 360° - 2×90° = 180°, so each is 90°.
- But wait — actually, if two lines cross and one angle is 90°, then all four angles are 90° (because vertical angles are equal, and adjacent angles sum to 180°).

So both `a`s are 90°?

Wait — let’s check the diagram carefully:

There’s a right angle mark at one intersection, and two angles labeled `a`. They are not adjacent to the right angle — they are opposite to each other.

So the two `a`s are vertically opposite to each other.

But since one angle is 90°, its vertical opposite is also 90°.

The other two angles (the ones not marked) would also be 90°, because:
- Angles on a straight line: 90° + x = 180° → x = 90°

So all angles are 90°.

Therefore, a = 90°

✔ Answer:
a = 90°

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✔ Problem 5:

> Diagram: Two lines intersect. One angle has a right angle (90°) symbol. Angles `a` and `b` are labeled. Given: angle a is double angle b.

- Right angle = 90°
- So one angle is 90° → its vertical opposite is also 90°.
- The remaining two angles (`a` and `b`) must be adjacent to 90° and form straight lines.
- So: a + b = 90° (since they lie on a straight line with the 90° angle)
- And: a = 2b

Substitute:
- $ 2b + b = 90 $
- $ 3b = 90 $
- $ b = 30 $
- $ a = 60 $

✔ Answer:
a = 60°, b = 30°

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✔ Problem 6:

> Diagram: Two lines intersect. One angle is 110°, and angles `a` and `b` labeled. Given: angle a is 10° more than angle b.

- The angle opposite to 110° is also 110° (vertical opposite).
- The adjacent angles to 110° must be 180° - 110° = 70°.
- So `a` and `b` are the two angles that are adjacent to 110° — and they are on a straight line with it.
- So: a + b = 70°
- And: a = b + 10°

Substitute:
- $ (b + 10) + b = 70 $
- $ 2b + 10 = 70 $
- $ 2b = 60 $
- $ b = 30 $
- $ a = 40 $

✔ Answer:
a = 40°, b = 30°

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📌 Final Answers Summary:

| Problem | a | b |
|--------|---------|---------|
| 1 | 130° | 50° |
| 2 | 80° | – |
| 3 | 50° | 30° |
| 4 | 90° | – |
| 5 | 60° | 30° |
| 6 | 40° | 30° |

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Let me know if you'd like this formatted as a printable answer sheet!