Worksheet on angles in triangles, including identifying impossible triangles and calculating missing angles.

Let’s solve this worksheet step by step.

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

We know that the sum of the interior angles in any triangle must be exactly 180°.

Let’s check each triangle:

Triangle 1 (orange): 73°, 68°, 39°

Add them:
73 + 68 = 141
141 + 39 = 180° → ✔ Possible

Triangle 2 (purple): 87°, 41.5°, 51.5°

Add them:
87 + 41.5 = 128.5
128.5 + 51.5 = 180° → ✔ Possible

Triangle 3 (blue): 28°, 46°, 107°

Add them:
28 + 46 = 74
74 + 107 = 181° → ✘ Impossible!

> Answer for Section A:
> The blue triangle is impossible because its angles add up to 181°, but the sum of angles in any triangle must be exactly 180°.

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## Section B: Find the missing angles in each of these triangles.

Again, use the rule: Sum of angles = 180°

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Triangle with angle `a`:

Right triangle → one angle is 90°, another is 47°.
So:
a + 90 + 47 = 180
a = 180 - 90 - 47 = 43°

✔ a = 43°

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Triangle with angle `b`:

Right triangle → one angle is 90°, another is 45°.
So:
b + 90 + 45 = 180
b = 180 - 90 - 45 = 45°

✔ b = 45°

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Triangle with angle `c`:

Angles: 74°, 36°, c
c = 180 - 74 - 36 =
180 - 110 = 70°

✔ c = 70°

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Triangle with angle `d`:

Angles: 101°, 27°, d
d = 180 - 101 - 27 =
180 - 128 = 52°

✔ d = 52°

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Triangle with angle `e`:

Angles: 36.5°, 51.2°, e
e = 180 - 36.5 - 51.2 =
First: 36.5 + 51.2 = 87.7
Then: 180 - 87.7 = 92.3°

✔ e = 92.3°

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Triangle with angle `f`:

Angles: 56.1°, 89°, f
f = 180 - 56.1 - 89 =
56.1 + 89 = 145.1
180 - 145.1 = 34.9°

✔ f = 34.9°

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## ✔ Final Answers:

Section A:

The blue triangle (with angles 28°, 46°, and 107°) is impossible because the sum of its angles is 181°, not 180°.

Section B:

- a = 43°
- b = 45°
- c = 70°
- d = 52°
- e = 92.3°
- f = 34.9°

You’re all set! 🎯