Let’s solve each problem one by one. We’ll use the rule that the sum of interior angles in a polygon depends on how many sides it has.
The formula is:
Sum of interior angles = (n – 2) × 180°, where
n is the number of sides.
We’ll find the missing angle
x by adding up all known angles and subtracting from the total sum.
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Problem 1: Quadrilateral (4 sides)
Angles given: 104°, 136°, 78°, and x.
Total sum for quadrilateral = (4 – 2) × 180° = 2 × 180° =
360°
Add known angles:
104 + 136 = 240
240 + 78 = 318
So, x = 360 – 318 =
42°
✔ Check: 104 + 136 + 78 + 42 = 360 → Correct!
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Problem 2: Hexagon (6 sides)
Angles given: 120°, 79°, 135°, 109°, 120°, and x.
Wait — let me count: The diagram shows 6 angles? Actually, looking again — it's a hexagon, so 6 sides → 6 angles.
Given angles: 120°, 79°, 135°, 109°, 120°, and x → that’s 6 angles. Good.
Total sum = (6 – 2) × 180° = 4 × 180° =
720°
Add known angles:
Start with 120 + 79 = 199
199 + 135 = 334
334 + 109 = 443
443 + 120 = 563
So, x = 720 – 563 =
157°
✔ Check: 120+79+135+109+120+157 = Let’s add step by step:
120+79=199; 199+135=334; 334+109=443; 443+120=563; 563+157=720 → Correct!
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Problem 3: Pentagon (5 sides)
Angles given: 112°, 112°, 121°, x, x → two angles are labeled x.
Total sum = (5 – 2) × 180° = 3 × 180° =
540°
Known angles: 112 + 112 + 121 = ?
112 + 112 = 224
224 + 121 = 345
So, the two x’s together = 540 – 345 =
195°
Since both are equal: x = 195 ÷ 2 =
97.5°
✔ Check: 112 + 112 + 121 + 97.5 + 97.5 =
112+112=224; 224+121=345; 97.5+97.5=195; 345+195=540 → Correct!
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Problem 4: Quadrilateral (4 sides)
Angles given: 94°, 104°, 90° (right angle), and x.
Total sum = 360° (as before)
Add known angles: 94 + 104 + 90 = ?
94 + 104 = 198
198 + 90 = 288
So, x = 360 – 288 =
72°
✔ Check: 94 + 104 + 90 + 72 = 360 → Correct!
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Final Answer:
1. x = 42°
2. x = 157°
3. x = 97.5°
4. x = 72°
Parent Tip: Review the logic above to help your child master the concept of interior angles of polygons worksheet.
