Finding missing angles worksheet - Free Printable

Let's solve the 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 measure:

- A: The angle is greater than 180° but less than 360° → Reflex angle
- B: There’s a small square symbol, indicating 90° → Right angle
- C: The angle is less than 90° → Acute angle
- D: The angle is between 90° and 180° → 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 these key facts:
- 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 = 90°

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#### (a)
Given: 22°, find a

These two angles form a straight line:
> a + 22° = 180°
> a = 180° − 22° = 158°

✔ a = 158°

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#### (b)
Given: 38°, right angle (90°), find b

The total angle at the corner is 90° (right angle).
So:
> b + 38° = 90°
> b = 90° − 38° = 52°

✔ b = 52°

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#### (c)
Given: 51°, right angle (90°), find c

This is a triangle-like shape with a right angle and 51°.
But actually, it's three lines forming angles around a point.

Wait — let's analyze:
There's a right angle (90°) and a 51° angle, and we're to find c, which is adjacent to them.

But looking closely: The vertical line and horizontal line form a right angle (90°), then another line cuts through.

So, the angles around the point must sum to 360°.

But here, we have:
- One angle is 51°
- One is 90° (right angle)
- And c is the remaining one?

Actually, the figure shows a vertical line and a diagonal line intersecting, with a 51° angle and a right angle marked.

But wait — the right angle is shown at the intersection of two perpendicular lines. Then a third line crosses, making a 51° angle.

Looking carefully:
It seems like c is part of a triangle or formed with the right angle.

Alternatively, think:
The angle between the vertical line and the diagonal is 51°, and there's a right angle between the vertical and horizontal.

So, the angle between the diagonal and horizontal line is:
> 90° − 51° = 39°

But that's not labeled.

Wait — the angle c is the one *opposite* the 51°, but it's not vertically opposite.

Let’s look again:
At the vertex, we have:
- A right angle (90°)
- A 51° angle
- And c is the other angle in the same "corner"

But they appear to be adjacent angles forming a full turn.

Wait — better approach:
The vertical line and the diagonal make a 51° angle. The vertical and horizontal make 90°. So the angle between diagonal and horizontal is 90° − 51° = 39°.

But c is the angle *between* the diagonal and the vertical, but on the other side?

Actually, c appears to be the angle adjacent to the 51° and the right angle.

Wait — maybe the total around the point is 360°.

But only three angles are visible? Let’s assume:

- One angle is 90° (right angle)
- One is 51°
- And c is the third angle?

But no — it looks like two lines cross: one vertical, one diagonal.

Then the angles around the point are:
- 51°
- c
- and others?

Wait — actually, the diagram shows a right angle symbol, so two lines are perpendicular. Then a third line cuts through, forming 51° with the vertical.

So, the angle c is the angle between the diagonal and the vertical, but on the other side.

Since the diagonal makes 51° with the vertical, then c is the other angle between the diagonal and the vertical, but since it's a straight line, the total on that side is 180°.

Wait — no. Actually, the vertical line has 180° along it.

So, if one side is 51°, then the other side (angle c) must be:

> c = 180° − 51° = 129°

But wait — there’s a right angle involved.

Alternative idea: The two lines are perpendicular (90°), and the third line forms 51° with one of them.

So, the angle c is the angle between the diagonal and the horizontal line?

Wait — perhaps this is a triangle.

Let me reinterpret:

From the diagram:
- Vertical line and horizontal line form a right angle (90°)
- A diagonal line goes from the corner, making a 51° angle with the vertical
- So, the angle between diagonal and horizontal is: 90° − 51° = 39°
- But c is labeled as the angle between the diagonal and the vertical, on the other side?

No — c is marked at the top, between the diagonal and the vertical line, but above.

If the diagonal makes 51° with the vertical on one side, then on the other side, it would be:

> c = 180° − 51° = 129°

But that doesn’t make sense because the total around the point should be 360°.

Wait — better way:
The two lines form a right angle. The third line splits the space.

But the 51° is given, and the right angle is there.

So, the angle c is the one that completes the straight line?

Wait — look at the diagram again:

It shows:
- A vertical line
- A horizontal line (forming 90°)
- A diagonal line going from bottom-left to top-right
- The angle between the diagonal and the vertical is 51°
- Angle c is the angle between the diagonal and the vertical on the top side

But since the vertical line is straight (180°), and one side is 51°, then the other side (angle c) must be:

> c = 180° − 51° = 129°

Yes! Because the diagonal cuts the vertical line into two parts: 51° and c, and together they make a straight line.

✔ c = 129°

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#### (d)
Given: 65°, 52°, find d

These three angles are on a straight line:
> d + 65° + 52° = 180°
> d = 180° − 65° − 52° = 180° − 117° = 63°

✔ d = 63°

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#### (e)
Two lines crossing, forming angles.

Given: 130°, find e and f

- e is vertically opposite to 130° → so e = 130°
- f is adjacent to 130°, so they form a straight line:
> f + 130° = 180° → f = 50°

Also, f is vertically opposite to the other 50°, so yes.

✔ e = 130°, f = 50°

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#### (f)
Three lines meeting at a point, angles given: 145°, 140°, find g

Sum of angles around a point = 360°

So:
> g = 360° − 145° − 140° = 360° − 285° = 75°

✔ g = 75°

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#### (g)
Triangle-like shape with angles: 73°, 38°, find h

The angles at the base: 73° and 38°, and h is the angle at the top.

But wait — the diagram shows a triangle with a horizontal line extended.

Actually, it looks like a triangle with a horizontal line drawn through the top vertex.

So, the angles at the top are split into h and 73°, and the other angle is 38°.

Wait — no. The figure shows:

- A triangle with base angles 73° and 38°?
- Or is it an angle at a point?

Wait — the diagram shows a triangle with a horizontal line passing through the top vertex.

But actually, the angles at the bottom are 73° and 38°, and h is the angle above.

Wait — more likely: It's a triangle with two known angles, and h is the third.

But the diagram shows a triangle with angles:
- One angle is 73°
- One is 38°
- And h is the third angle

So, in a triangle, angles add to 180°:
> h + 73° + 38° = 180°
> h = 180° − 111° = 69°

✔ h = 69°

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#### (h)
Three lines meeting at a point, angles given: 78°, 85°, 130°, find i

Sum around a point = 360°

So:
> i = 360° − 78° − 85° − 130° = 360° − 293° = 67°

✔ i = 67°

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#### (i)
Two lines crossing, with a right angle (90°) marked, and angles 82° and 73°, find j

First, note: There's a right angle symbol, so one angle is 90°.

The angles around the point:
We see:
- 82°
- 73°
- 90°
- and j

Wait — but 82° + 73° + 90° = 245°, so j = 360° − 245° = 115°?

But let's check the diagram.

Actually, the right angle is marked, so two lines are perpendicular.

Then a third line crosses them.

Wait — but there are only two lines shown: crossing, forming four angles.

One of them is marked as 82°, another as 73°, and a right angle.

But a right angle is 90°, so if one angle is 90°, and another is 82°, and another is 73°, that can't be — unless it's not all around the point.

Wait — the diagram shows:

- Two lines crossing
- One angle is 82°
- Another is 73°
- A right angle is marked — so one of the angles is 90°

But 82°, 73°, 90° — that's already over 245°, and there are only four angles.

But if one angle is 90°, then vertically opposite is also 90°.

So, two angles are 90°.

Now, the other two angles must add to 180° (since 360° − 180° = 180°).

But we’re given 82° and 73° — but 82° + 73° = 155° ≠ 180°

So contradiction.

Wait — maybe the 82° and 73° are adjacent?

But the diagram shows:

- One angle is 82°
- Adjacent to it is 73°
- And a right angle is marked — so 90°

Wait — could be: the two lines are not perpendicular? But the right angle symbol is there.

Ah! Wait — the right angle is marked at the intersection — so the two lines are perpendicular.

Therefore, the four angles are:
- 90°, 90°, 90°, 90°? No — only two pairs.

Wait — when two lines are perpendicular, all four angles are 90°.

But here, we have 82° and 73° — so that can't be.

Unless the right angle is not at the intersection?

Wait — the diagram shows:

- Two lines crossing
- At the intersection, a small square (right angle) is marked
- Then one angle is labeled 82°, another 73°, and j is the unknown

But if the lines are perpendicular, all angles must be 90°.

So either the right angle is not at the intersection, or it's a typo.

Wait — perhaps the right angle is not between the two crossing lines, but part of a different configuration.

Wait — re-read: the diagram shows two lines crossing, forming angles. One angle is 82°, another is 73°, and a right angle is marked.

But if two lines cross, they form two pairs of vertically opposite angles.

So if one angle is 82°, its opposite is 82°, and the adjacent ones are 180° − 82° = 98°.

Similarly for 73°.

But we have both 82° and 73°, and a right angle.

So perhaps the right angle is not at the intersection?

Wait — maybe the right angle is formed by one of the lines and a third line?

But only two lines are shown.

Wait — perhaps the diagram has two lines crossing, and the right angle is between one of the lines and a third direction?

No — it's unclear.

Wait — look again: the right angle is marked at the intersection, so the two lines are perpendicular.

Therefore, all angles are 90°.

But then why are 82° and 73° labeled?

Ah! Maybe the labels are not at the intersection.

Wait — perhaps the 82° and 73° are not at the intersection.

But the diagram shows:

- Two lines crossing
- At the intersection, a right angle is marked
- Then one of the angles is labeled 82°
- Another is labeled 73°
- And j is labeled

But if the lines are perpendicular, all angles are 90°, so 82° and 73° cannot be correct.

Unless the right angle is not between the two lines?

Wait — perhaps the right angle is formed by a third line?

Wait — the diagram might show three lines.

Wait — looking at the image: it shows two lines crossing, and a right angle symbol at the intersection.

Then one angle is labeled 82°, another 73°, and j.

But if the lines are perpendicular, all angles are 90°, so 82° and 73° don't make sense.

Unless the right angle is not at the intersection.

Wait — maybe the right angle is between the two lines, so they are perpendicular, so angles are 90°.

But then 82° and 73° must be errors.

Wait — perhaps the 82° and 73° are not the angles at the intersection, but something else.

Wait — no, the labels are placed at the corners.

Perhaps the diagram is showing that one of the angles is 82°, but it's adjacent to the right angle.

But if the lines are perpendicular, the angles are 90°, so no.

I think there's a mistake in interpretation.

Wait — perhaps the two lines are not perpendicular, but one of the angles is 90° due to a different reason.

But the right angle symbol is at the intersection, so the two lines are perpendicular.

Therefore, all angles at the intersection are 90°.

But then labeling 82° and 73° is inconsistent.

Unless the labels are not at the intersection.

Wait — perhaps the diagram shows:

- Two lines crossing
- One of the angles is 82°
- The adjacent angle is 73°
- But that can't happen because 82° + 73° = 155° < 180°, so the third angle would be 25°, but we have a right angle.

This is confusing.

Wait — perhaps the right angle is not at the intersection, but somewhere else.

But the symbol is at the intersection.

Wait — maybe the diagram has a right angle, and then two other angles.

But the only way this makes sense is if the two lines are not perpendicular.

But the right angle symbol implies they are.

Wait — perhaps the right angle is between one line and a third line?

But only two lines are shown.

I think there's a misinterpretation.

Wait — looking at the image: the two lines cross, and at the intersection, a right angle is marked, meaning the two lines are perpendicular.

So the four angles are all 90°.

But then why label 82° and 73°?

Unless the labels are not for the angles at the intersection.

But they are placed at the corners.

Wait — perhaps the 82° and 73° are not the angles at the intersection, but the angles between the lines and a third line?

But no third line.

Wait — perhaps the diagram shows that the two lines are crossing, and the angles are:
- One angle is 82°
- Another is 73°
- And a right angle is marked — so 90°
- And j is the fourth

But sum: 82 + 73 + 90 + j = 360
→ 245 + j = 360 → j = 115°

But that would mean the angles are not symmetric.

But if two lines cross, opposite angles are equal.

So if one angle is 82°, opposite is 82°; adjacent is 98°.

Similarly, if one is 73°, opposite is 73°, adjacent is 107°.

But we can't have both unless it's not two lines.

Ah! Wait — the diagram might show three lines meeting at a point.

Yes! That makes sense.

So three lines meet at a point.

One of the angles is 82°, another is 73°, and a right angle (90°) is marked.

And j is the missing angle.

Sum around a point = 360°

So:
> j = 360° − 82° − 73° − 90° = 360° − 245° = 115°

✔ j = 115°

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✔ Final Answers:

#### 1. Name the angles:
- A: Reflex angle
- B: Right angle
- C: Acute angle
- D: Obtuse angle

#### 2. Missing angles:
- (a) a = 158°
- (b) b = 52°
- (c) c = 129°
- (d) d = 63°
- (e) e = 130°, f = 50°
- (f) g = 75°
- (g) h = 69°
- (h) i = 67°
- (i) j = 115°

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✔ Summary Table:

| Question | Answer |
|--------|--------|
| a | 158° |
| b | 52° |
| c | 129° |
| d | 63° |
| e | 130° |
| f | 50° |
| g | 75° |
| h | 69° |
| i | 67° |
| j | 115° |

Let me know if you'd like a visual explanation or diagrams!