Geometry worksheet featuring twelve problems where students must calculate the value of x based on triangle angle properties.

To solve for x in each triangle, we use the Triangle Angle Sum Theorem, which states:

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

We’ll apply this to each problem one by one.

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1)

Angles: 58°, 47°, x°
→ 58 + 47 + x = 180
→ 105 + x = 180
→ x = 75

✔ Answer: x = 75

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2)

Angles: x°, 96°, 21°
→ x + 96 + 21 = 180
→ x + 117 = 180
→ x = 63

✔ Answer: x = 63

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3)

Right triangle → one angle is 90°, another is 31°, third is (3x - 1)°
→ 90 + 31 + (3x - 1) = 180
→ 121 + 3x - 1 = 180
→ 120 + 3x = 180
→ 3x = 60
→ x = 20

✔ Answer: x = 20

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4)

Angles: 21°, 34°, x°
→ 21 + 34 + x = 180
→ 55 + x = 180
→ x = 125

✔ Answer: x = 125

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5)

Angles: 100°, (2x + 3)°, 51°
→ 100 + (2x + 3) + 51 = 180
→ 154 + 2x = 180
→ 2x = 26
→ x = 13

✔ Answer: x = 13

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6)

Angles: 94°, 60°, 2x°
→ 94 + 60 + 2x = 180
→ 154 + 2x = 180
→ 2x = 26
→ x = 13

✔ Answer: x = 13

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7)

Angles: 52°, 43°, x°
→ 52 + 43 + x = 180
→ 95 + x = 180
→ x = 85

✔ Answer: x = 85

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8)

Angles: x°, 2x°, 3x°
→ x + 2x + 3x = 180
→ 6x = 180
→ x = 30

✔ Answer: x = 30

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9)

Right triangle → one angle = 90°, others: (2x - 2)° and (x + 5)°
→ 90 + (2x - 2) + (x + 5) = 180
→ 90 + 2x - 2 + x + 5 = 180
→ 93 + 3x = 180
→ 3x = 87
→ x = 29

✔ Answer: x = 29

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10)

Angles: 10°, 23°, x°
→ 10 + 23 + x = 180
→ 33 + x = 180
→ x = 147

✔ Answer: x = 147

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11)

Equilateral triangle? All angles equal → x°, x°, x°
→ x + x + x = 180
→ 3x = 180
→ x = 60

✔ Answer: x = 60

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12)

Angles: (x + 40)°, (3x - 17)°, (2x - 5)°
→ (x + 40) + (3x - 17) + (2x - 5) = 180
→ x + 3x + 2x + 40 - 17 - 5 = 180
→ 6x + 18 = 180
→ 6x = 162
→ x = 27

✔ Answer: x = 27

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## ✔ Final Answers:

1) 75
2) 63
3) 20
4) 125
5) 13
6) 13
7) 85
8) 30
9) 29
10) 147
11) 60
12) 27

Let me know if you’d like a diagram explanation for any specific one!