Angles In Quadrilaterals (Year 6) | CGP Plus - Free Printable

Let's solve each of the problems step by step.

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Part 1: Angles in Quadrilaterals

We know that the sum of the interior angles in any quadrilateral is 360°.

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#### 1. Orange Quadrilateral (a)
Given angles:
- 67°
- Two right angles = 90° each

So:
$$
a = 360^\circ - (67^\circ + 90^\circ + 90^\circ) = 360^\circ - 247^\circ = \boxed{113^\circ}
$$

✔ a = 113°

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#### 2. Green Quadrilateral (b)
Given angles:
- 90° (right angle)
- 74°
- 117°

So:
$$
b = 360^\circ - (90^\circ + 74^\circ + 117^\circ) = 360^\circ - 281^\circ = \boxed{79^\circ}
$$

✔ b = 79°

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#### 3. Blue Quadrilateral (c)
Given angles:
- 55°
- 111°
- 107°

So:
$$
c = 360^\circ - (55^\circ + 111^\circ + 107^\circ) = 360^\circ - 273^\circ = \boxed{87^\circ}
$$

✔ c = 87°

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#### 4. Pink Quadrilateral (d)
Given angles:
- 47°
- 89°
- 82°

So:
$$
d = 360^\circ - (47^\circ + 89^\circ + 82^\circ) = 360^\circ - 218^\circ = \boxed{142^\circ}
$$

✔ d = 142°

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#### 5. Orange "Arrow" Shape (e)
This looks like a quadrilateral with a missing angle labeled 'e'. But it's drawn as a triangle with an extra line — actually, this is a quadrilateral formed by extending one side. Let’s look carefully.

The shape has three angles given:
- 79°
- 38°
- 27°

But wait — this appears to be a triangle, but the figure is not closed properly? Actually, no — the angle marked e is at the "dent", so it's part of a concave quadrilateral.

Wait — let's check: It's a four-sided figure (quadrilateral), and the sum must still be 360°.

But the three outer angles are 79°, 38°, and 27°. The fourth angle is e, which is reflex (greater than 180°).

Wait — the angle labeled 239° in the next shape is reflex, so maybe this one is too?

No — here, the angle e is the internal angle at the "inward" point.

Actually, this is a quadrilateral, and the angles are:

- 79°
- 38°
- 27°
- e (unknown)

So:
$$
e = 360^\circ - (79^\circ + 38^\circ + 27^\circ) = 360^\circ - 144^\circ = \boxed{216^\circ}
$$

But wait — that seems large. However, if it's a concave quadrilateral, internal angles can be greater than 180°.

But looking at the diagram: the angle e is the internal angle at the "pointed inward" corner.

So yes, it could be reflex.

But let’s double-check:
Sum of angles: 79 + 38 + 27 = 144 → So e = 360 − 144 = 216°

✔ e = 216°

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#### 6. Green "Arrow" Shape (f)
This is another quadrilateral with angles:

- 48°
- 34°
- 239° (reflex angle)

Note: 239° is already a reflex angle.

So total of known angles:
48° + 34° + 239° = 321°

Then:
$$
f = 360^\circ - 321^\circ = \boxed{39^\circ}
$$

✔ f = 39°

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Part 2: Parallelograms

In a parallelogram:
- Opposite angles are equal.
- Adjacent angles add up to 180° (since consecutive angles are supplementary).
- Opposite sides are parallel.

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#### First Parallelogram:
Given:
- One angle = 108°
- Another angle = 72°

We see that:
- 108° and 72° are adjacent → 108 + 72 = 180° → good.

Now:
- a is opposite to 108° → so a = 108°
- b is opposite to 72° → so b = 72°

✔ a = 108°, b = 72°

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#### Second Parallelogram:
Given:
- One angle = 57°

Adjacent angle (c) = 180° − 57° = 123°

So:
- c = 123°
- d is opposite to 57° → d = 57°
- e is opposite to c → e = 123°

✔ c = 123°, d = 57°, e = 123°

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✔ Final Answers:

#### Quadrilaterals:
- a = 113°
- b = 79°
- c = 87°
- d = 142°
- e = 216°
- f = 39°

#### Parallelograms:
- a = 108°, b = 72°
- c = 123°, d = 57°, e = 123°

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✔ Summary Table:

| Letter | Value |
|--------|-------|
| a | 113° |
| b | 79° |
| c | 87° |
| d | 142° |
| e | 216° |
| f | 39° |
| a (para) | 108° |
| b (para) | 72° |
| c (para) | 123° |
| d (para) | 57° |
| e (para) | 123° |

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