Angles interactive worksheet for Grade 5 - Free Printable

Let’s go through each angle one by one. We’ll look at the shape of the angle and use what we know about angle types:

- Acute = less than 90°
- Right = exactly 90° (often marked with a small square)
- Obtuse = more than 90° but less than 180°
- Straight = exactly 180° (looks like a straight line)
- Reflex = more than 180° but less than 360°
- Complete = exactly 360° (full circle)

We also label each angle using three letters — the middle letter is always the vertex (the point where the two lines meet).

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Problem 2:
Angle has rays ON and OM, meeting at O. There’s a small square → that means it’s a right angle.
Label: ∠MON or ∠NOM (vertex in the middle). Let’s pick ∠MON.

→ Type: Right angle
→ Label: ∠MON

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Problem 3:
Angle at Q, between P-Q-R. The arc shows it’s bigger than 180°? Wait — no! Look again: the arc is drawn on the *inside*, and it looks like it’s more than 90° but less than 180°. Actually, from the drawing, it’s clearly obtuse (between 90° and 180°).
Label: ∠PQR (vertex Q in the middle).

→ Type: Obtuse angle
→ Label: ∠PQR

Wait — let me double-check. In problem 3, the angle shown is the one inside the “V” shape — yes, it’s greater than 90°, so obtuse. Correct.

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Problem 4:
Points C-O-D are in a straight line. Angle is 180°.
Label: ∠COD (or ∠DOC)

→ Type: Straight angle
→ Label: ∠COD

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Problem 5:
Angle at O, between U-O-V. It says 260° — that’s more than 180°, less than 360° → reflex angle.
Label: ∠UOV (vertex O in middle)

→ Type: Reflex angle
→ Label: ∠UOV

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Problem 6:
Angle at L, between K-L-M. Given as 245° → again, more than 180°, less than 360° → reflex.
Label: ∠KLM

→ Type: Reflex angle
→ Label: ∠KLM

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Problem 7:
Angle at R, between Q-R-S. Looks like it’s more than 90°, less than 180° → obtuse.
Label: ∠QRS

→ Type: Obtuse angle
→ Label: ∠QRS

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Problem 8:
It shows a full circle with 360° → complete angle. Only one ray shown, but it implies a full rotation.
Label: Since there’s only one labeled point besides the center, maybe just call it “angle at the center” — but typically for 360°, we can say ∠XYZ if points were given… here, only one direction is labeled. But since it’s a full turn, we can still label it based on the ray — perhaps ∠AAB? No, better to think: usually, for a complete angle, you might not have three distinct points. But in this case, since it’s drawn with one ray going out, and a full circle, we can assume the start and end are the same ray. So maybe label it as ∠XXX? That doesn’t work.

Actually, looking back at the diagram — it’s just a single ray with a full circle around it. In such cases, sometimes it’s labeled by the vertex alone, but the instruction says “label each angle that it forms, for example: ∠ABC”. So we need three letters. Hmm.

Wait — perhaps the vertex is the center, and the ray goes to some point — but only one letter is given? Actually, in the image, it’s just an arrow pointing right, with a circle around the starting point. Maybe we can imagine two points: say, the vertex is O, and the ray goes to A, then back to A after full turn — but that’s not standard.

Alternatively, perhaps the problem expects us to recognize it’s a complete angle and label it generically. But let’s check the pattern: all others have three letters. For this one, since no other points are labeled, maybe we can’t form a proper ∠ABC. But wait — in many textbooks, a complete angle is often just referred to by its measure or as “a full angle”, but the worksheet asks to label it like ∠ABC.

Looking again — actually, in problem 8, there’s only one labeled endpoint? No, the diagram shows a horizontal ray to the right, and a circle around the origin. Probably, the vertex is implied, and we can make up labels? But that’s not good.

Wait — perhaps I missed something. Let me re-express: in problem 8, it's likely that the angle is formed by a ray rotating fully around its endpoint. So if we consider the starting position and ending position are the same, we could label it as ∠AOA, but that’s unusual.

But note: in some contexts, they accept labeling with the vertex and any two coinciding points — but that’s messy.

Alternatively, maybe the diagram intends for us to see it as a zero-degree angle plus 360, but no.

Actually, let’s look at common practice: for a complete angle, if only one ray is shown, sometimes it’s labeled with the vertex and the same point twice — but that’s not standard.

Perhaps there’s a mistake? Or maybe in this context, since it’s 360°, and no other points, we can just write "Complete angle" and for label, leave it blank? But the table requires both.

Wait — another idea: in problem 8, although only one direction is drawn, the angle is defined by the full rotation, so we can consider two positions: initial and final, which are the same. So if we call the vertex O, and the ray goes to point A initially and finally, then ∠AOA — but that’s degenerate.

I recall that in some curricula, they do allow ∠AAA for a complete angle, though it’s rare.

But let’s check online or standard examples — actually, upon second thought, in many worksheets, when a full circle is shown with one ray, they might expect you to label it as ∠XYZ where X and Z are the same point — but since no points are labeled except implicitly, perhaps we should invent labels? That seems wrong.

Wait — looking back at the original image description: in problem 8, it’s “360°” with a circle and one arrow. Probably, the vertex is the center, and the ray defines the direction. To follow the format, perhaps we can assume the vertex is O, and the ray goes to A, so the angle is from OA back to OA — so ∠AOA. But that’s awkward.

Alternatively, maybe the problem allows just stating the type and for label, writing "complete angle at center" — but the instruction says "for example: ∠ABC".

This is tricky. Let me see if there’s another way. Perhaps in this case, since it’s a special case, they expect:

Type: Complete angle
Label: (leave blank?) — but the table has space.

Wait — I found a better approach: in some systems, a complete angle is labeled by the vertex alone, but the worksheet specifies three-letter notation.

Perhaps for consistency, we can use the same point for first and last. Let’s do that.

Assume the vertex is O, and the ray ends at A. Then the angle from OA to OA (full turn) is ∠AOA.

But that’s unconventional. However, for the sake of completing the worksheet, I’ll go with that.

So:

→ Type: Complete angle
→ Label: ∠AOA (assuming A is the endpoint of the ray, O is vertex)

But in the diagram, no letters are given for problem 8! Oh no — I just realized: in problem 8, there are no labeled points at all! The diagram is just a circle with an arrow, and "360°" written below.

That’s a problem. How to label without points?

Perhaps it’s an oversight, or perhaps we’re supposed to infer. Maybe the vertex is implied, and we can use generic letters.

To resolve this, I’ll assume the vertex is O, and the ray goes to point A, so label is ∠AOA.

Some sources do use this notation for full angles.

Alternatively, perhaps the label is not required for this one, but the table has columns.

Another idea: in problem 8, since it’s a full circle, and no specific rays, maybe it’s not labeled with three letters — but the instruction says "also label each angle that it forms", implying all should be labeled.

I think the safest bet is to use ∠XXX or something, but that’s silly.

Wait — let’s look at problem 9: it has X,Y,Z — so labeled.

For problem 8, perhaps it’s intended to be recognized as complete angle, and for label, since no points, maybe write "N/A" — but that’s not following instructions.

Perhaps I misread: in the user’s message, for problem 8, it’s described as “360°” with a circle and arrow — no letters mentioned. So probably, we can’t form a proper ∠ABC. But to comply, I’ll use hypothetical points.

Let me define: let the vertex be O, and the ray extend to point A. Then the complete angle is ∠AOA.

I’ll go with that.

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Problem 9:
Angle at Y, between X-Y-Z. Small square → right angle.
Label: ∠XYZ

→ Type: Right angle
→ Label: ∠XYZ

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Now, let’s compile all answers carefully.

Double-checking:

1) Already done: Acute, ∠AOC — correct.

2) Right angle, ∠MON — yes.

3) Obtuse, ∠PQR — yes.

4) Straight, ∠COD — yes.

5) Reflex (260°), ∠UOV — yes.

6) Reflex (245°), ∠KLM — yes.

7) Obtuse, ∠QRS — yes.

8) Complete (360°), label: since no points, but must provide, I'll use ∠AOA assuming A is on the ray, O vertex. But to be precise, perhaps the worksheet expects just the type, and for label, leave blank? But the table has cells.

Upon second thought, in many similar worksheets, for a full angle with no specific points, they might accept "complete angle" and no label, but here the column is "LABEL the angle", so probably expected to have something.

I recall that sometimes it's labeled as "angle of 360 degrees" but not in ∠ABC form.

To stay consistent, I'll use ∠OOO — but that's worse.

Best solution: since the ray is drawn, let's say the vertex is the center, call it O, and the endpoint of the ray is A, so the angle from OA to OA is ∠AOA. I think that's acceptable for this level.

So:

→ Type: Complete angle
→ Label: ∠AOA

9) Right angle, ∠XYZ — yes.

Now, writing final answers in order.

Final Answer:
2) Type: Right angle, Label: ∠MON
3) Type: Obtuse angle, Label: ∠PQR
4) Type: Straight angle, Label: ∠COD
5) Type: Reflex angle, Label: ∠UOV
6) Type: Reflex angle, Label: ∠KLM
7) Type: Obtuse angle, Label: ∠QRS
8) Type: Complete angle, Label: ∠AOA
9) Type: Right angle, Label: ∠XYZ

Note: For problem 8, since no points are labeled in the diagram, ∠AOA is assumed with O as vertex and A as a point on the ray. If your teacher prefers different labeling, adjust accordingly, but this follows the three-letter convention.