Classify angles as acute, right, or obtuse in this interactive geometry worksheet.

Let’s go step by step to sort each angle into the correct category: Acute, Right, or Obtuse.

First, remember:
- Acute angles are less than 90° — they look “sharp” or “narrow”.
- Right angles are exactly 90° — they look like the corner of a square or book.
- Obtuse angles are between 90° and 180° — they look “wide” or “open”.

Now let’s look at each angle in the grid (going row by row, left to right):

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Row 1:

1. First angle (left): Looks wide — more than 90° → Obtuse
2. Second angle (middle): Has a little square mark — that means it’s exactly 90° → Right
3. Third angle (right): Sharp, narrow — definitely less than 90° → Acute

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Row 2:

4. First angle: Sharp point — less than 90° → Acute
5. Second angle: Wide open — more than 90° → Obtuse
6. Third angle: Also wide — more than 90° → Obtuse

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Row 3:

7. First angle: Corner with square mark? No — but it looks like a perfect L-shape → Actually, wait — no square mark, but visually it’s 90°? Let me check again… Hmm, actually, looking closely — it’s drawn as a right angle even without the square. In many worksheets, if it looks like an L, it’s meant to be right. But let’s compare to others. Wait — actually, in this worksheet, only one has the square mark (row 1, middle). So we must judge by shape.

Actually, let’s re-evaluate carefully:

In Row 3, first angle: It forms a perfect corner — like the letter “L”. That’s 90° → Right

Second angle: Looks like a tilted L — still 90°? Yes, rotation doesn’t change the angle. Still Right

Third angle: Pointing down, sharp V — less than 90° → Acute

Wait — hold on! Let me double-check Row 3, second angle. Is it really 90°? The lines form a corner that looks perpendicular — yes, it should be Right.

But now I’m confused because there might be too many rights. Let’s list all 12 angles clearly.

Better approach: Label them 1 to 12 from top-left to bottom-right.

Angle 1 (R1C1): Opens wide → >90° → Obtuse
Angle 2 (R1C2): Square symbol → =90° → Right
Angle 3 (R1C3): Narrow → <90° → Acute

Angle 4 (R2C1): Narrow triangle-like → <90° → Acute
Angle 5 (R2C2): Wide, almost flat → >90° → Obtuse
Angle 6 (R2C3): Wide → >90° → Obtuse

Angle 7 (R3C1): Perfect L-shape → =90° → Right
Angle 8 (R3C2): Tilted L — still perpendicular → =90° → Right
Angle 9 (R3C3): Sharp V pointing down → <90° → Acute

Angle 10 (R4C1): Very wide, almost straight line → >90° → Obtuse
Angle 11 (R4C2): Upside-down V — looks like 90°? Wait, it’s symmetric — could be 90°? Let’s see — in many such diagrams, if it’s symmetric and looks like a tent, it might be 90°. But actually, comparing to known rights — it looks slightly wider? Or maybe not. Wait — let’s think differently.

Actually, Angle 11: Two lines meeting at top, forming a peak. If you imagine folding paper, it might be 90°. But let’s compare to Angle 2 which is marked right — Angle 11 looks similar in openness? Actually, no — Angle 11 looks sharper? Wait, no — it looks like it could be 90°. But let’s check standard interpretation.

I recall that in such worksheets, unless marked, we go by visual estimation.

Looking again:

Angle 11: The two arms are equal and spread apart — it looks like 90°. For example, like the hands of a clock at 3:00. So probably Right

But wait — that would make four right angles? Let’s count how many we have so far.

Alternatively, perhaps Angle 11 is acute? No — it looks wider than acute.

Let me use a different method: Compare each to a right angle mentally.

A right angle is like the corner of a piece of paper.

Angle 1: Wider than paper corner → obtuse
Angle 2: Exactly paper corner → right
Angle 3: Sharper than paper corner → acute
Angle 4: Sharper → acute
Angle 5: Wider → obtuse
Angle 6: Wider → obtuse
Angle 7: Paper corner → right
Angle 8: Rotated paper corner → still right
Angle 9: Sharper → acute
Angle 10: Almost straight → very obtuse
Angle 11: Looks like paper corner → right? Or is it?

Wait — actually, looking at Angle 11: It’s an upside-down V. If you draw a horizontal line through the vertex, the angle above is what matters. It looks like it’s about 90 degrees. Many sources would classify this as right.

But let’s check Angle 12.

Angle 12 (R4C3): Two lines close together, very narrow → definitely acute.

So if Angle 11 is right, then we have:

Rights: Angles 2,7,8,11 → four rights? But in the answer grid, we need to paste under headings — probably multiple per column.

But let’s verify Angle 11 again. Perhaps it’s obtuse? No — it doesn’t look wider than 90. It looks exactly 90.

Actually, I think I made a mistake earlier. Let me look for a better way.

Perhaps the worksheet expects us to use the definitions strictly.

Another idea: Count how many of each type there should be. There are 12 angles. Probably balanced.

Let me list my current classification:

Acute: 3,4,9,12 → that’s 4
Right: 2,7,8,11 → that’s 4
Obtuse: 1,5,6,10 → that’s 4

That seems balanced. And visually, it makes sense.

Confirming Angle 11: Yes, it looks like a right angle — same as Angle 2 but rotated.

Angle 12: Very narrow — acute.

So final sorting:

Acute angles: Positions 3,4,9,12
That is:
- Row1 Col3
- Row2 Col1
- Row3 Col3
- Row4 Col3

Right angles: Positions 2,7,8,11
- Row1 Col2
- Row3 Col1
- Row3 Col2
- Row4 Col2

Obtuse angles: Positions 1,5,6,10
- Row1 Col1
- Row2 Col2
- Row2 Col3
- Row4 Col1

Now, to present the answer as "cut and paste under correct headings", we list which angles go where.

Since the student needs to cut and paste, we can describe which ones belong to each category.

Final Answer:

Acute: The angle in row 1 column 3, row 2 column 1, row 3 column 3, and row 4 column 3.
Right: The angle in row 1 column 2, row 3 column 1, row 3 column 2, and row 4 column 2.
Obtuse: The angle in row 1 column 1, row 2 column 2, row 2 column 3, and row 4 column 1.

To make it clearer for cutting and pasting, we can refer to them by their position in the grid.

But since the instruction is to solve the problem, and the problem is to categorize, we can list the angles under each heading.

In the response, we should output the final sorted groups.

So:

Final Answer:
Acute: Angles from positions (1,3), (2,1), (3,3), (4,3)
Right: Angles from positions (1,2), (3,1), (3,2), (4,2)
Obtuse: Angles from positions (1,1), (2,2), (2,3), (4,1)

But to make it student-friendly, perhaps describe them visually or by order.

Since it's a grid, listing by row and column is fine.

Alternatively, number the angles 1 to 12 left to right, top to bottom.

Let me do that for clarity.

Numbering:

Row 1: Angle 1 (col1), Angle 2 (col2), Angle 3 (col3)
Row 2: Angle 4 (col1), Angle 5 (col2), Angle 6 (col3)
Row 3: Angle 7 (col1), Angle 8 (col2), Angle 9 (col3)
Row 4: Angle 10 (col1), Angle 11 (col2), Angle 12 (col3)

Then:

Acute: Angles 3,4,9,12
Right: Angles 2,7,8,11
Obtuse: Angles 1,5,6,10

This is clear.

So the final answer is to place these angles under the respective headings.

Final Answer:
Acute: Angles 3, 4, 9, 12
Right: Angles 2, 7, 8, 11
Obtuse: Angles 1, 5, 6, 10