Find the missing angle in each quadrilateral.
Worksheet with 12 quadrilateral diagrams, each showing some angles and asking to find the missing angle measures.
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Step-by-step solution for: Identifying Quadrilaterals Worksheets - Worksheets Library
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Show Answer Key & Explanations
Step-by-step solution for: Identifying Quadrilaterals Worksheets - Worksheets Library
We are given 12 quadrilaterals, each with three angles labeled (as ∠BAD, ∠ABC, ∠BCD, ∠CDA — which correspond to angles at vertices A, B, C, D respectively), and one angle missing. We need to find the measure of the missing angle in each case.
Key fact:
The sum of the interior angles of any quadrilateral is always:
$$
360^\circ
$$
So for each problem, add the three known angles and subtract from 360° to get the missing angle.
Let’s go one by one:
---
1) Given:
∠BAD = ?
∠ABC = 59.1°
∠BCD = 71.4°
∠CDA = 96.2°
Sum of known angles:
59.1 + 71.4 + 96.2 =
59.1 + 71.4 = 130.5
130.5 + 96.2 = 226.7
Missing ∠BAD = 360 − 226.7 = 133.3°
---
2)
∠BAD = 92.8°
∠ABC = 90.4°
∠BCD = 82.0°
∠CDA = ?
Sum 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°
---
3)
∠BAD = 90.4°
∠ABC = 100.5°
∠BCD = ?
∠CDA = 95.1°
Sum 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°
---
4)
∠BAD = 68.6°
∠ABC = 114.5°
∠BCD = ?
∠CDA = 81.2°
Sum 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°
---
5)
∠BAD = ?
∠ABC = 102.7°
∠BCD = 75.8°
∠CDA = 86.7°
Sum 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°
---
6)
∠BAD = 125.5°
∠ABC = ?
∠BCD = 99.2°
∠CDA = 66.7°
Sum 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°
---
7)
∠BAD = 84.6°
∠ABC = ?
∠BCD = 110.4°
∠CDA = 72.6°
Sum 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°
---
8)
∠BAD = 94.9°
∠ABC = 97.2°
∠BCD = 72.3°
∠CDA = ?
Sum known: 94.9 + 97.2 + 72.3 =
94.9 + 97.2 = 192.1
192.1 + 72.3 = 264.4
Missing ∠CDA = 360 − 264.4 = 95.6°
---
9)
∠BAD = 89.3°
∠ABC = 102.8°
∠BCD = 76.0°
∠CDA = ?
Sum 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°
---
10)
∠BAD = 99.3°
∠ABC = ?
∠BCD = 73.7°
∠CDA = 97.7°
Sum 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°
---
11)
∠BAD = ?
∠ABC = 103.2°
∠BCD = 58.3°
∠CDA = 109.3°
Sum 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°
---
12)
∠BAD = 99.1°
∠ABC = 88.8°
∠BCD = ?
∠CDA = 74.7°
Sum 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°
---
Now double-check a few to avoid arithmetic errors:
- #1: 59.1 + 71.4 = 130.5; +96.2 = 226.7 → 360 − 226.7 = 133.3 ✔
- #5: 102.7 + 75.8 = 178.5; +86.7 = 265.2; 360 − 265.2 = 94.8 ✔
- #11: 103.2 + 58.3 = 161.5; +109.3 = 270.8; 360 − 270.8 = 89.2 ✔
All seem correct.
Final Answer:
1) 133.3°
2) 94.8°
3) 74.0°
4) 95.7°
5) 94.8°
6) 68.6°
7) 92.4°
8) 95.6°
9) 91.9°
10) 89.3°
11) 89.2°
12) 97.4°
Key fact:
The sum of the interior angles of any quadrilateral is always:
$$
360^\circ
$$
So for each problem, add the three known angles and subtract from 360° to get the missing angle.
Let’s go one by one:
---
1) Given:
∠BAD = ?
∠ABC = 59.1°
∠BCD = 71.4°
∠CDA = 96.2°
Sum of known angles:
59.1 + 71.4 + 96.2 =
59.1 + 71.4 = 130.5
130.5 + 96.2 = 226.7
Missing ∠BAD = 360 − 226.7 = 133.3°
---
2)
∠BAD = 92.8°
∠ABC = 90.4°
∠BCD = 82.0°
∠CDA = ?
Sum 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°
---
3)
∠BAD = 90.4°
∠ABC = 100.5°
∠BCD = ?
∠CDA = 95.1°
Sum 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°
---
4)
∠BAD = 68.6°
∠ABC = 114.5°
∠BCD = ?
∠CDA = 81.2°
Sum 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°
---
5)
∠BAD = ?
∠ABC = 102.7°
∠BCD = 75.8°
∠CDA = 86.7°
Sum 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°
---
6)
∠BAD = 125.5°
∠ABC = ?
∠BCD = 99.2°
∠CDA = 66.7°
Sum 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°
---
7)
∠BAD = 84.6°
∠ABC = ?
∠BCD = 110.4°
∠CDA = 72.6°
Sum 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°
---
8)
∠BAD = 94.9°
∠ABC = 97.2°
∠BCD = 72.3°
∠CDA = ?
Sum known: 94.9 + 97.2 + 72.3 =
94.9 + 97.2 = 192.1
192.1 + 72.3 = 264.4
Missing ∠CDA = 360 − 264.4 = 95.6°
---
9)
∠BAD = 89.3°
∠ABC = 102.8°
∠BCD = 76.0°
∠CDA = ?
Sum 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°
---
10)
∠BAD = 99.3°
∠ABC = ?
∠BCD = 73.7°
∠CDA = 97.7°
Sum 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°
---
11)
∠BAD = ?
∠ABC = 103.2°
∠BCD = 58.3°
∠CDA = 109.3°
Sum 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°
---
12)
∠BAD = 99.1°
∠ABC = 88.8°
∠BCD = ?
∠CDA = 74.7°
Sum 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°
---
Now double-check a few to avoid arithmetic errors:
- #1: 59.1 + 71.4 = 130.5; +96.2 = 226.7 → 360 − 226.7 = 133.3 ✔
- #5: 102.7 + 75.8 = 178.5; +86.7 = 265.2; 360 − 265.2 = 94.8 ✔
- #11: 103.2 + 58.3 = 161.5; +109.3 = 270.8; 360 − 270.8 = 89.2 ✔
All seem correct.
Final Answer:
1) 133.3°
2) 94.8°
3) 74.0°
4) 95.7°
5) 94.8°
6) 68.6°
7) 92.4°
8) 95.6°
9) 91.9°
10) 89.3°
11) 89.2°
12) 97.4°
Parent Tip: Review the logic above to help your child master the concept of classifying quadrilaterals worksheet.
