Finding missing angles worksheet - Free Printable

Here is the complete solution to the "Angles Revision" worksheet, with explanations for each part.

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1. Name the angles below.

This section asks you to identify the type of angle shown in each diagram.

* A: This angle is greater than 180° but less than 360°. It's called a Reflex Angle.
* B: This angle has a small square symbol, which indicates it measures exactly 90°. It's called a Right Angle.
* C: This angle is smaller than 90°. It's called an Acute Angle.
* D: This angle is larger than 90° but smaller than 180°. It's called an Obtuse Angle.

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2. Find the missing angles in the questions below.

We will use the key rules provided:
* Angles on a straight line add up to 180°.
* Angles around a point add up to 360°.
* Vertically opposite angles are equal.
* A right angle is 90°.

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#### (a) Find `a`

* The angles `22°` and `a` are on a straight line.
* Therefore, they must add up to 180°.
* Calculation: `a = 180° - 22° = 158°`

> Answer: `a = 158°`

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#### (b) Find `b`

* The diagram shows a right angle (90°) split into two parts: `b` and `38°`.
* So, `b + 38° = 90°`.
* Calculation: `b = 90° - 38° = 52°`

> Answer: `b = 52°`

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#### (c) Find `c`

* The angles `c`, `90°` (right angle), and `51°` are all around a point on a straight line (they form a straight angle).
* Therefore, `c + 90° + 51° = 180°`.
* Calculation: `c = 180° - 90° - 51° = 39°`

> Answer: `c = 39°`

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#### (d) Find `d`

* The angles `65°`, `52°`, and `d` are on a straight line.
* So, `65° + 52° + d = 180°`.
* Calculation: `d = 180° - 65° - 52° = 63°`

> Answer: `d = 63°`

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#### (e) Find `e` and `f`

* These are vertically opposite angles formed by two intersecting lines.
* Vertically opposite angles are equal.
* We are given one angle is `130°`. The angle opposite to it is `f`, so `f = 130°`.
* The other pair of vertically opposite angles (`e` and the unmarked angle) must also be equal.
* All four angles around the point add up to 360°.
* So, `130° + f + e + (the other angle) = 360°`.
* Since `f = 130°` and the other angle equals `e`, we have: `130° + 130° + e + e = 360°`.
* Simplify: `260° + 2e = 360°`.
* Calculation: `2e = 360° - 260° = 100°`, so `e = 50°`.

> Answer: `e = 50°`, `f = 130°`

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#### (f) Find `g`

* The angles `140°`, `145°`, and `g` are around a point.
* All angles around a point add up to 360°.
* So, `140° + 145° + g = 360°`.
* Calculation: `g = 360° - 140° - 145° = 75°`

> Answer: `g = 75°`

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#### (g) Find `h`

* The angles `h`, `73°`, and `38°` are on a straight line.
* So, `h + 73° + 38° = 180°`.
* Calculation: `h = 180° - 73° - 38° = 69°`

> Answer: `h = 69°`

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#### (h) Find `i`

* The angles `78°`, `85°`, `130°`, and `i` are around a point.
* So, `78° + 85° + 130° + i = 360°`.
* Calculation: `i = 360° - 78° - 85° - 130° = 67°`

> Answer: `i = 67°`

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#### (i) Find `j`

* The diagram shows a right angle (90°), `82°`, `73°`, and `j` around a point.
* So, `90° + 82° + 73° + j = 360°`.
* Calculation: `j = 360° - 90° - 82° - 73° = 115°`

> Answer: `j = 115°`

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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) `a = 158°`
- (b) `b = 52°`
- (c) `c = 39°`
- (d) `d = 63°`
- (e) `e = 50°`, `f = 130°`
- (f) `g = 75°`
- (g) `h = 69°`
- (h) `i = 67°`
- (i) `j = 115°`

All solutions follow from the fundamental rules of angles on a straight line (sum to 180°) and angles around a point (sum to 360°), along with the properties of right angles and vertically opposite angles.