Geometry Worksheets | Polygons Worksheets - Free Printable

Let’s solve each problem one by one.

We’re dealing with quadrilaterals (4-sided shapes).
The key rule:
> The sum of all interior angles in any quadrilateral is always 360 degrees.

So for each shape, we’ll add up the three known angles and subtract from 360 to find the missing angle.

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Problem 1:

Given:
∠BAD = ?
∠ABC = 59.1°
∠BCD = 71.4°
∠CDA = 96.2°

Add known angles:
59.1 + 71.4 + 96.2 =
→ 59.1 + 71.4 = 130.5
→ 130.5 + 96.2 = 226.7

Missing angle ∠BAD = 360 - 226.7 = 133.3°

✔ Check: 133.3 + 59.1 + 71.4 + 96.2 = 360 → Correct.

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Problem 2:

Given:
∠BAD = 92.8°
∠ABC = 90.4°
∠BCD = 82.0°
∠CDA = ?

Add known:
92.8 + 90.4 + 82.0 =
→ 92.8 + 90.4 = 183.2
→ 183.2 + 82.0 = 265.2

Missing ∠CDA = 360 - 265.2 = 94.8°

✔ Check: 92.8 + 90.4 + 82.0 + 94.8 = 360 → Correct.

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Problem 3:

Given:
∠BAD = 90.4°
∠ABC = 100.5°
∠BCD = ?
∠CDA = 95.1°

Add known:
90.4 + 100.5 + 95.1 =
→ 90.4 + 100.5 = 190.9
→ 190.9 + 95.1 = 286.0

Missing ∠BCD = 360 - 286.0 = 74.0°

✔ Check: 90.4 + 100.5 + 74.0 + 95.1 = 360 → Correct.

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Problem 4:

Given:
∠BAD = 68.6°
∠ABC = 114.5°
∠BCD = ?
∠CDA = 81.2°

Add known:
68.6 + 114.5 + 81.2 =
→ 68.6 + 114.5 = 183.1
→ 183.1 + 81.2 = 264.3

Missing ∠BCD = 360 - 264.3 = 95.7°

✔ Check: 68.6 + 114.5 + 95.7 + 81.2 = 360 → Correct.

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Problem 5:

Given:
∠BAD = ?
∠ABC = 102.7°
∠BCD = 75.8°
∠CDA = 86.7°

Add known:
102.7 + 75.8 + 86.7 =
→ 102.7 + 75.8 = 178.5
→ 178.5 + 86.7 = 265.2

Missing ∠BAD = 360 - 265.2 = 94.8°

✔ Check: 94.8 + 102.7 + 75.8 + 86.7 = 360 → Correct.

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Problem 6:

Given:
∠BAD = 125.5°
∠ABC = ?
∠BCD = 99.2°
∠CDA = 66.7°

Add known:
125.5 + 99.2 + 66.7 =
→ 125.5 + 99.2 = 224.7
→ 224.7 + 66.7 = 291.4

Missing ∠ABC = 360 - 291.4 = 68.6°

✔ Check: 125.5 + 68.6 + 99.2 + 66.7 = 360 → Correct.

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Problem 7:

Given:
∠BAD = 84.6°
∠ABC = ?
∠BCD = 110.4°
∠CDA = 72.6°

Add known:
84.6 + 110.4 + 72.6 =
→ 84.6 + 110.4 = 195.0
→ 195.0 + 72.6 = 267.6

Missing ∠ABC = 360 - 267.6 = 92.4°

✔ Check: 84.6 + 92.4 + 110.4 + 72.6 = 360 → Correct.

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Problem 8:

Given:
∠BAD = 94.8°
∠ABC = 97.2°
∠BCD = 72.3°
∠CDA = ?

Add known:
94.8 + 97.2 + 72.3 =
→ 94.8 + 97.2 = 192.0
→ 192.0 + 72.3 = 264.3

Missing ∠CDA = 360 - 264.3 = 95.7°

✔ Check: 94.8 + 97.2 + 72.3 + 95.7 = 360 → Correct.

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Problem 9:

Given:
∠BAD = 89.3°
∠ABC = 102.8°
∠BCD = 76.0°
∠CDA = ?

Add known:
89.3 + 102.8 + 76.0 =
→ 89.3 + 102.8 = 192.1
→ 192.1 + 76.0 = 268.1

Missing ∠CDA = 360 - 268.1 = 91.9°

✔ Check: 89.3 + 102.8 + 76.0 + 91.9 = 360 → Correct.

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Problem 10:

Given:
∠BAD = 99.3°
∠ABC = ?
∠BCD = 73.7°
∠CDA = 97.7°

Add known:
99.3 + 73.7 + 97.7 =
→ 99.3 + 73.7 = 173.0
→ 173.0 + 97.7 = 270.7

Missing ∠ABC = 360 - 270.7 = 89.3°

✔ Check: 99.3 + 89.3 + 73.7 + 97.7 = 360 → Correct.

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Problem 11:

Given:
∠BAD = ?
∠ABC = 103.2°
∠BCD = 58.3°
∠CDA = 109.3°

Add known:
103.2 + 58.3 + 109.3 =
→ 103.2 + 58.3 = 161.5
→ 161.5 + 109.3 = 270.8

Missing ∠BAD = 360 - 270.8 = 89.2°

✔ Check: 89.2 + 103.2 + 58.3 + 109.3 = 360 → Correct.

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Problem 12:

Given:
∠BAD = 99.1°
∠ABC = 88.8°
∠BCD = ?
∠CDA = 74.7°

Add known:
99.1 + 88.8 + 74.7 =
→ 99.1 + 88.8 = 187.9
→ 187.9 + 74.7 = 262.6

Missing ∠BCD = 360 - 262.6 = 97.4°

✔ Check: 99.1 + 88.8 + 97.4 + 74.7 = 360 → Correct.

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Final Answer:

1) ∠BAD = 133.3°
2) ∠CDA = 94.8°
3) ∠BCD = 74.0°
4) ∠BCD = 95.7°
5) ∠BAD = 94.8°
6) ∠ABC = 68.6°
7) ∠ABC = 92.4°
8) ∠CDA = 95.7°
9) ∠CDA = 91.9°
10) ∠ABC = 89.3°
11) ∠BAD = 89.2°
12) ∠BCD = 97.4°