Identifying Angles (Year 3) | CGP Plus - Free Printable

Let's solve the "Identifying Angles" worksheet step by step and explain each answer clearly.

---

Part 1: True or False Questions

We are given three shapes:
- Shape A: Regular hexagon (6 sides)
- Shape B: Triangle (appears to be an acute triangle)
- Shape C: Irregular pentagon (5 sides)

#### Statement 1:
> Every angle in Shape A is greater than a right angle.
✔ Answer: False

Explanation:
Shape A is a regular hexagon. In a regular hexagon, each interior angle measures:

$$
\text{Interior angle} = \frac{(n - 2) \times 180^\circ}{n} = \frac{(6 - 2) \times 180^\circ}{6} = \frac{4 \times 180^\circ}{6} = 120^\circ
$$

Since $120^\circ > 90^\circ$, each angle is greater than a right angle.
So this statement should be True, but wait — let’s double-check.

Wait! The shape appears to be a regular hexagon, so all angles are $120^\circ$, which is greater than a right angle (90°). So actually, this statement is TRUE.

But the image shows the word "False" circled in red — that seems incorrect.

✘ Correction: This should be True, not False.

Let’s reevaluate based on what's visually shown.

Looking at Shape A: It's a regular hexagon, so yes, each internal angle is $120^\circ$ → greater than $90^\circ$. So:
> ✔ True

But the worksheet says "False" is circled — possibly a mistake? Let’s keep going.

#### Statement 2:
> Shape B is the only shape where all of its angles are smaller than a right angle.
✔ Answer: True

Explanation:
Shape B is a triangle. It looks like an acute triangle (all angles less than $90^\circ$). Since it's a triangle, the sum of angles is $180^\circ$. If all angles are less than $90^\circ$, it's possible (e.g., 60°, 60°, 60°).

Now check other shapes:
- Shape A: All angles are $120^\circ$ → greater than $90^\circ$
- Shape C: Looks like it has some right angles and possibly one acute angle

So only Shape B has all angles less than $90^\circ$. Therefore:
> ✔ True

#### Statement 3:
> Shape C has exactly two right angles and one acute angle.
✔ Answer: False

Explanation:
Shape C is a pentagon with five angles. Looking at the shape:
- Two corners look like right angles (90°)
- One corner looks acute (less than 90°)
- But there are five angles total — we’ve accounted for only three so far.
- The remaining two angles appear to be obtuse (greater than 90°), possibly even reflex?

But the statement says: "exactly two right angles and one acute angle."

That would mean only three angles described — but there are five angles in a pentagon.

So unless the other two are also right or acute, this is not accurate.

Moreover, if it has two right angles and one acute, then the sum of those three is already more than $90^\circ + 90^\circ + 90^\circ = 270^\circ$, but we need to consider the total sum.

Sum of interior angles of a pentagon:

$$
(5 - 2) \times 180^\circ = 540^\circ
$$

Suppose two right angles ($90^\circ$ each) = $180^\circ$
One acute angle (say $60^\circ$) → total so far: $240^\circ$

Remaining two angles must add up to $540^\circ - 240^\circ = 300^\circ$ → average $150^\circ$, so both obtuse.

So the shape does have two right angles, one acute, and two obtuse.

But the statement says: "exactly two right angles and one acute angle" — this is partially true, but it doesn’t say anything about the others, so it might be misleading.

But in logic, if a statement says “has exactly two right angles and one acute angle,” it implies only those three types, but doesn't specify whether others exist.

However, since it has more than one type of angle, and the statement claims only those three, but fails to mention the other two angles, the claim is incomplete.

But the key word is "exactly" — meaning no more than two right angles and no more than one acute angle.

From visual inspection:
- Yes, two right angles
- Yes, one acute angle
- And two obtuse angles

So it does have exactly two right angles and one acute angle — even though it has other angles too.

So the statement is true?

Wait — the phrase "has exactly two right angles and one acute angle" means:
- Exactly two right angles ✔
- Exactly one acute angle ✔
- The rest can be any other type (like obtuse)

So yes, this is true.

But again, the worksheet shows "False" circled in teal — perhaps it's wrong?

Let’s recheck the shape.

Looking closely at Shape C:
- Top-left: looks like a right angle
- Bottom-left: looks like a right angle
- Top-right: sharp point → likely acute
- Bottom-right: wide → obtuse
- Middle top: another wide angle → obtuse

So:
- Two right angles ✔
- One acute angle ✔
- Two obtuse angles ✔

So the statement: "Shape C has exactly two right angles and one acute angle" — is TRUE, because it has exactly two right angles and exactly one acute angle.

But the worksheet says "False" is circled — that seems incorrect.

Possibility: Maybe the top-left and bottom-left aren’t actually right angles?

But they look like squares — probably intended to be right angles.

Alternatively, maybe the shape is drawn such that one is slightly off.

But assuming standard interpretation:
> ✔ Statement 3 is True

But the worksheet marks it as False — likely a mistake.

Wait — perhaps I misread. Let's go back.

Actually, the worksheet already has answers circled in different colors:
- First statement: False (red)
- Second: True (orange)
- Third: False (teal)

But from our analysis:
1. Shape A: all angles are $120^\circ$ → greater than $90^\circ$ → True
2. Shape B: only one with all angles < $90^\circ$ → True
3. Shape C: has exactly two right angles and one acute → True

But the worksheet says:
- 1: False ✘ (should be True)
- 2: True ✔
- 3: False ✘ (should be True)

So either the answers are wrong, or the shapes are interpreted differently.

Wait — maybe Shape A is not regular?

But it looks symmetric — a regular hexagon.

Unless it's a concave hexagon? No, it's convex.

Alternatively, perhaps Shape A has some angles less than 90°?

No — in a regular hexagon, all angles are $120^\circ$.

So why is "False" circled?

Possibility: The question says "Every angle in Shape A is greater than a right angle."

If it's true, then the answer should be True.

But the worksheet says False — that's wrong.

Maybe the shape is not regular?

But it looks regular.

Alternatively, could it be a different polygon?

No — six sides, regular appearance.

So I believe the correct answers should be:
1. True (every angle in A is > 90°)
2. True (B is the only one with all angles < 90°)
3. True (C has exactly two right angles and one acute)

But the worksheet shows:
- 1: False ✘
- 2: True ✔
- 3: False ✘

So likely, the provided answers are incorrect, or the shapes are drawn differently.

But let's assume the shapes are as intended.

Wait — Shape B is a triangle. Is it really acute?

Yes — all angles look less than 90°. So yes.

But is Shape A really all angles > 90°?

Yes — regular hexagon: 120° each → greater than 90° → True

So the first answer being False is incorrect.

Similarly, Shape C: two right angles, one acute — yes → True

So the worksheet's answers seem to have errors.

But perhaps I'm missing something.

Wait — Shape C has five angles. The statement says: "has exactly two right angles and one acute angle"

That doesn't say anything about the other two — so if it has two right, one acute, and two obtuse, then it does have exactly two right and one acute — so the statement is true.

So why is it marked False?

Possibility: The shape might have more than two right angles?

But it looks like only two.

Or maybe the top-left isn't a right angle?

Let’s suppose the top-left angle is obtuse, and the bottom-left is right, etc.

But without exact measurements, we go by visual.

Given the context, likely the intended correct answers are:

1. True (A: all angles > 90°)
2. True (B: only shape with all angles < 90°)
3. True (C: has exactly two right and one acute)

But the worksheet shows otherwise.

Perhaps it's a trick — maybe Shape A is not regular?

But it looks regular.

Alternatively, maybe Shape A is a concave hexagon? No, it's convex.

I think the worksheet's answers may be incorrect, or the shapes are meant to be interpreted differently.

But let’s move on to Part 2, which is clearer.

---

Part 2: Circle the angles that fit the description

We are given four shapes and asked to identify specific angles.

#### Shape 1: Purple trapezoid (left top)
Label: "A right angle"

Look at the angles:
- Left-bottom and left-top: look like right angles (square corners)
- Right-top and right-bottom: wider → obtuse

So circle the two left angles — both are right angles.

✔ Circle the two angles on the left side.

#### Shape 2: Red diamond (right top)
Label: "An angle greater than a right angle"

This is a rhombus-like shape — all sides equal, opposite angles equal.

The top and bottom angles look wide → obtuse (>90°)
The left and right angles look acute (<90°)

So angles greater than a right angle are the top and bottom angles.

✔ Circle the top and bottom angles

#### Shape 3: Green pentagon (left bottom)
Label: "An acute angle"

Look at the angles:
- The top-left angle is very sharp → acute
- Other angles: look like right or obtuse

So circle the top-left angle

✔ Circle the sharp top-left angle

#### Shape 4: Blue arrow-shaped polygon (right bottom)
Label: "An angle less than or equal to a right angle"

This shape has:
- A pointy tip at the front → acute angle
- The side angles: some look like right angles, others obtuse

Let’s analyze:
- The front tip → acute
- The back angles: one looks like a right angle (square corner)
- Others: may be obtuse

So angles less than or equal to 90° include:
- The acute tip
- Any right angles

Looking at the shape:
- The top-left and bottom-left angles look like right angles
- The front tip is acute
- The back angles are obtuse

So circle:
- The front tip (acute)
- The top-left and bottom-left (right angles)

✔ Circle the front tip, top-left, and bottom-left angles

---

✔ Final Answers Summary:

#### Part 1: True or False

1. Every angle in Shape A is greater than a right angle.
→ True (since regular hexagon has 120° angles)
✘ Worksheet says False → Incorrect

2. Shape B is the only shape where all of its angles are smaller than a right angle.
→ True (it's an acute triangle; others have ≥90° angles)
✔ Correctly marked as True

3. Shape C has exactly two right angles and one acute angle.
→ True (visually: two right, one acute, two obtuse)
✘ Worksheet says False → Incorrect

#### Part 2: Circle angles

1. Purple trapezoid – right angles:
→ Circle the left-side angles (both are right angles)

2. Red diamond – angles > 90°:
→ Circle the top and bottom angles (obtuse)

3. Green pentagon – acute angle:
→ Circle the top-left sharp angle

4. Blue arrow – angles ≤ 90°:
→ Circle the front tip (acute), top-left, and bottom-left (right angles)

---

🟩 Conclusion:

The worksheet contains errors in Part 1:
- Statement 1 should be True, not False
- Statement 3 should be True, not False

But Part 2 is correctly designed and can be solved accurately.

Let me know if you'd like a corrected version of the worksheet!