Angles in Triangles (B) | 4th Grade PDF Geometry Worksheets - Free Printable

Let's solve the problem step by step.

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Section A: Which one of these is an impossible triangle? Explain why.

We are given three triangles with their angles labeled. To determine if a triangle is possible, we use the Triangle Angle Sum Theorem, which states:

> The sum of the interior angles in any triangle is 180°.

Let’s check each triangle:

#### Triangle 1 (Yellow):
Angles: 73°, 68°, 39°
Sum = 73 + 68 + 39 = 180° ✔
This is a valid triangle.

#### Triangle 2 (Purple):
Angles: 87°, 41.5°, 51.5°
Sum = 87 + 41.5 + 51.5 = 180° ✔
This is also valid.

#### Triangle 3 (Blue):
Angles: 28°, 46°, 107°
Sum = 28 + 46 + 107 = 181° ✘
This exceeds 180°, so it’s impossible.

✔ Answer: The blue triangle is impossible because the sum of its angles is 181°, which is greater than 180°. A triangle cannot have angles that add up to more than 180°.

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Section B: Find the missing angles in each triangle.

We’ll use the fact that:
> Sum of angles in a triangle = 180°

Also, remember:
- A right angle = 90°
- An angle marked with a square is a right angle.

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#### a) Triangle with angles: 90° (right angle), 47°, and missing angle a

Sum = 90 + 47 + a = 180
→ 137 + a = 180
→ a = 180 - 137 = 43°

✔ a = 43°

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#### b) Triangle with angles: 90°, 45°, and missing angle b

Sum = 90 + 45 + b = 180
→ 135 + b = 180
→ b = 180 - 135 = 45°

✔ b = 45°

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#### c) Triangle with angles: 74°, 36°, and missing angle c

Sum = 74 + 36 + c = 180
→ 110 + c = 180
→ c = 180 - 110 = 70°

✔ c = 70°

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#### d) Triangle with angles: 101°, 27°, and missing angle d

Sum = 101 + 27 + d = 180
→ 128 + d = 180
→ d = 180 - 128 = 52°

✔ d = 52°

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#### e) Triangle with angles: 36.5°, 51.2°, and missing angle e

Sum = 36.5 + 51.2 + e = 180
→ 87.7 + e = 180
→ e = 180 - 87.7 = 92.3°

✔ e = 92.3°

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#### f) Triangle with angles: 56.1°, 89°, and missing angle f

Sum = 56.1 + 89 + f = 180
→ 145.1 + f = 180
→ f = 180 - 145.1 = 34.9°

✔ f = 34.9°

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✔ Final Answers:

#### Section A:
The blue triangle (with angles 28°, 46°, 107°) is impossible because the sum of its angles is 181°, which is more than 180°. A triangle must have angles that add up to exactly 180°.

#### Section B:
- a = 43°
- b = 45°
- c = 70°
- d = 52°
- e = 92.3°
- f = 34.9°

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