Let’s solve each problem step by step. We’ll use the rule:
>
Sum of interior angles = (Number of sides - 2) × 180°
Then, we add up all the given angles and set them equal to that sum to find the missing angle(s).
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Problem 1: Quadrilateral (4 sides)
Sum = (4-2) × 180° = 360°
Given angles: 125°, 68°, 62°, x°
Add known: 125 + 68 + 62 = 255
So: 255 + x = 360 → x = 360 - 255 =
105
✔ Answer for #1:
x = 105
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Problem 2: Quadrilateral (4 sides)
Sum = 360°
Given: 105°, 106°, 72°, x°
Add known: 105 + 106 + 72 = 283
x = 360 - 283 =
77
✔ Answer for #2:
x = 77
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Problem 3: Quadrilateral (4 sides)
Sum = 360°
Given: x°, 98°, 120°, 80°
Add known: 98 + 120 + 80 = 298
x = 360 - 298 =
62
✔ Answer for #3:
x = 62
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Problem 4: Pentagon (5 sides)
Sum = (5-2) × 180 = 540°
Angles: (x - 27)°, (x - 15)°, 125°, 112°, (x + 30)°
Add them:
(x - 27) + (x - 15) + 125 + 112 + (x + 30)
= x + x + x + (-27 -15 + 125 + 112 + 30)
= 3x + ( -42 + 267 ) = 3x + 225
Set equal to 540:
3x + 225 = 540
3x = 540 - 225 = 315
x = 315 ÷ 3 =
105
✔ Answer for #4:
x = 105
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Problem 5: Pentagon (5 sides)
Sum = 540°
Angles: x°, 115°, 95°, 115°, 130°
Add known: 115 + 95 + 115 + 130 = 455
x = 540 - 455 =
85
✔ Answer for #5:
x = 85
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Problem 6: Quadrilateral (4 sides)
Sum = 360°
Angles: 60°, x°, x°, x° → so 60 + 3x = 360
3x = 300 → x =
100
✔ Answer for #6:
x = 100
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Problem 7: Pentagon (5 sides)
Sum = 540°
Angles: x°, 107°, 75°, (x + 12)°, (x - 14)°
Add them:
x + 107 + 75 + (x + 12) + (x - 14)
= x + x + x + (107 + 75 + 12 - 14)
= 3x + (194 - 14) = 3x + 180
Set equal to 540:
3x + 180 = 540
3x = 360 → x =
120
✔ Answer for #7:
x = 120
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Problem 8: Hexagon (6 sides)
Sum = (6-2) × 180 = 720°
Angles: (2x - 50)°, (x + 40)°, 80°, (x + 20)°, x°, 150°
Add them:
(2x - 50) + (x + 40) + 80 + (x + 20) + x + 150
Combine like terms:
2x + x + x + x = 5x
Constants: -50 + 40 + 80 + 20 + 150 = let's compute step by step:
-50 + 40 = -10
-10 + 80 = 70
70 + 20 = 90
90 + 150 = 240
So total: 5x + 240
Set equal to 720:
5x + 240 = 720
5x = 480 → x =
96
✔ Answer for #8:
x = 96
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Final Answer:
1. x = 105
2. x = 77
3. x = 62
4. x = 105
5. x = 85
6. x = 100
7. x = 120
8. x = 96
Parent Tip: Review the logic above to help your child master the concept of angles of polygons worksheets.
