Finding missing angles worksheet - Free Printable

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

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## 1. Name the angles below

We need to identify each angle type based on its measure or appearance:

- A: This is a reflex angle — it’s greater than 180° but less than 360° (you can see it wraps around more than half a circle).
- B: This has a square corner — that’s a right angle (exactly 90°).
- C: This is clearly smaller than 90° — an acute angle.
- D: This is larger than 90° but less than 180° — 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 add up to 180°
> - Angles around a point add up to 360°
> - Also, vertically opposite angles are equal.

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(a)

We have a straight line with two angles: 22° and angle `a`.

Since they’re on a straight line:
> `a + 22° = 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`.

So:
> `b + 38° = 90°`
> → `b = 90° - 38° = 52°`

✔ b = 52°

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(c)

We have a right angle (90°) at the vertex, and one angle is 51°. The other is angle `c`.

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`.

Total = 180°:
> `65° + 52° + d = 180°`
> → `117° + d = 180°`
> → `d = 180° - 117° = 63°`

✔ d = 63°

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(e)

Two lines crossing — vertically opposite angles are equal.

We’re given one angle is 130°. Angle `e` is vertically opposite to it → so `e = 130°`.

Angle `f` is adjacent to 130° on a straight line → so:
> `f + 130° = 180°`
> → `f = 50°`

✔ e = 130°, f = 50°

*(Note: f could also be found using vertically opposite angles — the angle opposite f is also 50°, since 180° - 130° = 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: 38°, 73°, and `h`.

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

✔ h = 69°

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(h)

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

Total = 360°:
> `78° + 85° + 130° + i = 360°`
> → `293° + i = 360°`
> → `i = 67°`

✔ i = 67°

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(i)

Three angles around a point: 82°, 73°, and `j`. But wait — there’s also a right angle symbol (90°)!

So total = 360°:
> `82° + 73° + 90° + j = 360°`
> → `245° + j = 360°`
> → `j = 115°`

✔ j = 115°

*(Note: If you didn’t notice the right angle, you’d get wrong answer. Always look for the little square!)*

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## ✔ Final Answers Summary:

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 = 130°, f = 50°
- g = 75°
- h = 69°
- i = 67°
- j = 115°

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Let me know if you want diagrams or explanations for any specific part! 😊