Angles Revision worksheet featuring questions on identifying and calculating angles, including straight lines and angles around a point.

Let’s solve this Angles Revision worksheet step by step.

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## 1. Name the angles below

We need to identify the type of each angle based on its shape and measure (even if not labeled numerically).

- A: This is a reflex angle — it’s greater than 180° but less than 360°. The arc goes the long way around.
- B: This has a square corner — that’s a right angle (exactly 90°).
- C: This is an acute angle — clearly less than 90°. So, acute angle.
- D: This is wider than a right angle but less than 180° — so it’s an obtuse angle.

✔ Answers:
- A: Reflex angle
- B: Right angle
- C: Acute angle
- D: Obtuse angle

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## 2. Find the missing angles

We’ll use two key rules:
> - Angles on a straight line = 180°
> - Angles around a point = 360°
> - Vertically opposite angles are equal.
> - Right angles = 90°

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(a)

We have a straight line with two angles: 22° and angle `a`.
They must add to 180°.

> a = 180° – 22° = 158°

✔ a = 158°

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(b)

This is a right angle (90°) split into two parts: 38° and angle `b`.

> b = 90° – 38° = 52°

✔ b = 52°

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(c)

We see a right angle (90°) at the center, and one angle is 51°. The other angle `c` is adjacent to it along the same straight line? Wait — actually, looking at the diagram, it seems like `c` and 51° are together forming a right angle (because there’s a square corner). So:

> c + 51° = 90°
> → c = 90° – 51° = 39°

✔ c = 39°

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(d)

Three angles on a straight line: 65°, 52°, and `d`.

> 65° + 52° + d = 180°
> → 117° + d = 180°
> → d = 180° – 117° = 63°

✔ d = 63°

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(e)

Two intersecting lines form vertically opposite angles. We’re given one angle as 130°, and we need to find `e` and `f`.

- Vertically opposite angles are equal → so the angle opposite 130° is also 130°.
- The other two angles (`e` and `f`) are equal (vertically opposite), and all four angles add up to 360°.

So:

> 130° + 130° + e + f = 360°
> → 260° + e + f = 360°
> → e + f = 100°
> Since e = f (vertically opposite),
> → e = f = 50°

✔ e = 50°, f = 50°

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(f)

Three angles around a point: 140°, 145°, and `g`.

> Total around a point = 360°
> → 140° + 145° + g = 360°
> → 285° + g = 360°
> → g = 360° – 285° = 75°

✔ g = 75°

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(g)

Three angles on a straight line: `h`, 73°, and 38°.

> h + 73° + 38° = 180°
> → h + 111° = 180°
> → h = 180° – 111° = 69°

✔ h = 69°

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(h)

Four angles around a point: 78°, 85°, 130°, and `i`.

> 78° + 85° + 130° + i = 360°
> → 293° + i = 360°
> → i = 360° – 293° = 67°

✔ i = 67°

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(i)

We have a right angle (90°) marked, and two other angles: 82° and 73°, and we need to find `j`.

Wait — let’s look carefully. All angles are around a point. There’s a right angle (90°), plus 82°, 73°, and `j`.

> 90° + 82° + 73° + j = 360°
> → 245° + j = 360°
> → j = 360° – 245° = 115°

✔ j = 115°

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## ✔ Final Answers:

1. Naming Angles:

- A: Reflex angle
- B: Right angle
- C: Acute angle
- D: Obtuse angle

2. Missing Angles:

- a = 158°
- b = 52°
- c = 39°
- d = 63°
- e = 50°
- f = 50°
- g = 75°
- h = 69°
- i = 67°
- j = 115°

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