Angles In Quadrilaterals — Use the Clues (Year 6) | CGP Plus - Free Printable

Let's solve each of the quadrilateral angle problems step by step. Remember, the sum of the interior angles in any quadrilateral is always 360°.

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🔷 Problem 1: Green Quadrilateral

Given:
- One angle = 125°
- One angle = 85°
- Angle a is double angle b

We need to find angles a and b.

Let’s denote:
- Let angle b = x
- Then angle a = 2x

Sum of all angles = 360°
So:
$$
125 + 85 + a + b = 360 \\
210 + 2x + x = 360 \\
210 + 3x = 360 \\
3x = 150 \\
x = 50
$$

So:
- b = 50°
- a = 2 × 50 = 100°

✔ Answer:
a = 100°, b = 50°

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🔷 Problem 2: Blue Quadrilateral (with right angle)

Given:
- One angle = 90° (right angle)
- One angle = 100°
- Angle c is 30° more than angle d

Let angle d = x
Then angle c = x + 30

Sum of angles:
$$
90 + 100 + c + d = 360 \\
190 + (x + 30) + x = 360 \\
190 + 2x + 30 = 360 \\
220 + 2x = 360 \\
2x = 140 \\
x = 70
$$

So:
- d = 70°
- c = 70 + 30 = 100°

✔ Answer:
c = 100°, d = 70°

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🔷 Problem 3: Orange Quadrilateral

Given:
- One angle = 45°
- Angles e, f, g are all equal

Let each of e, f, g = x

Sum:
$$
e + f + g + 45 = 360 \\
x + x + x + 45 = 360 \\
3x + 45 = 360 \\
3x = 315 \\
x = 105
$$

So:
- e = f = g = 105°

✔ Answer:
e = 105°, f = 105°, g = 105°

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🔷 Problem 4: Teal Quadrilateral

Given:
- Two angles: 68° and 102°
- Angle h is 40° more than angle i

Let angle i = x
Then angle h = x + 40

Sum:
$$
68 + 102 + h + i = 360 \\
170 + (x + 40) + x = 360 \\
170 + 2x + 40 = 360 \\
210 + 2x = 360 \\
2x = 150 \\
x = 75
$$

So:
- i = 75°
- h = 75 + 40 = 115°

✔ Answer:
h = 115°, i = 75°

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🔷 Problem 5: Red Quadrilateral

Given:
- Two angles: 125° and 109°
- Angle j is half of angle k

Let angle j = x
Then angle k = 2x

Sum:
$$
125 + 109 + j + k = 360 \\
234 + x + 2x = 360 \\
234 + 3x = 360 \\
3x = 126 \\
x = 42
$$

So:
- j = 42°
- k = 84°

✔ Answer:
j = 42°, k = 84°

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🔷 Problem 6: Purple Triangle (Wait! It's not a quadrilateral!)

⚠️ Wait — this shape is not a quadrilateral; it's a triangle with an extra line inside forming a "V" shape. But let's read carefully:

It shows a triangle with two 55° angles and a point labeled y inside, where y is four times angle x.

But actually, looking at the diagram: It's a triangle with one vertex split into two parts: angle x and angle y, and two base angles of 55°.

But the triangle has three angles: two are 55°, and the third is made up of x and y.

So total interior angles of a triangle = 180°

Let’s assume:
- Two angles = 55° each
- Third angle = x + y
- Given: y = 4x

So:
$$
55 + 55 + (x + y) = 180 \\
110 + x + y = 180 \\
x + y = 70
$$

Substitute y = 4x:
$$
x + 4x = 70 \\
5x = 70 \\
x = 14 \\
y = 4 × 14 = 56
$$

✔ Answer:
x = 14°, y = 56°

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| a, b | a = 100°, b = 50° |
| c, d | c = 100°, d = 70° |
| e, f, g | e = f = g = 105° |
| h, i | h = 115°, i = 75° |
| j, k | j = 42°, k = 84° |
| x, y | x = 14°, y = 56° |

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📝 Notes:

- All quadrilaterals have 360° total.
- The last shape is a triangle, not a quadrilateral, but the logic still applies using triangle angle sum = 180°.
- Always use the clues and set up equations based on relationships.

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