Adding Angles Worksheet 4Th Grade - Printable Secrets Exposed - Free Printable

Let’s solve each problem using the linear pair theorem.

> 💡 Remember: A linear pair means two angles that sit next to each other on a straight line. Their measures add up to 180 degrees.

We’ll go one by one, set up the equation (angle 1 + angle 2 = 180), and solve for x.

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Problem 1:
Angles: (2x + 5)° and 65°
Equation:
(2x + 5) + 65 = 180
→ 2x + 70 = 180
→ 2x = 110
→ x = 55

✔ Check: 2(55)+5 = 115; 115 + 65 = 180 → Correct!

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Problem 2:
Angles: 136° and (4x + 12)°
Equation:
136 + (4x + 12) = 180
→ 4x + 148 = 180
→ 4x = 32
→ x = 8

✔ Check: 4(8)+12 = 44; 136 + 44 = 180 → Correct!

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Problem 3:
Angles: 45° and (5x + 25)°
Equation:
45 + (5x + 25) = 180
→ 5x + 70 = 180
→ 5x = 110
→ x = 22

✔ Check: 5(22)+25 = 135; 45 + 135 = 180 → Correct!

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Problem 4:
Angles: (7x - 8)° and 76°
Equation:
(7x - 8) + 76 = 180
→ 7x + 68 = 180
→ 7x = 112
→ x = 16

✔ Check: 7(16)-8 = 104; 104 + 76 = 180 → Correct!

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Problem 5:
Angles: (3x - 17)° and 122°
Equation:
(3x - 17) + 122 = 180
→ 3x + 105 = 180
→ 3x = 75
→ x = 25

✔ Check: 3(25)-17 = 58; 58 + 122 = 180 → Correct!

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Problem 6:
Angles: 80° and (8x - 36)°
Equation:
80 + (8x - 36) = 180
→ 8x + 44 = 180
→ 8x = 136
→ x = 17

✔ Check: 8(17)-36 = 100; 80 + 100 = 180 → Correct!

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Problem 7:
Angles: (4x - 30)° and 106°
Equation:
(4x - 30) + 106 = 180
→ 4x + 76 = 180
→ 4x = 104
→ x = 26

✔ Check: 4(26)-30 = 74; 74 + 106 = 180 → Correct!

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Problem 8:
Angles: (x + 40)° and 52°
Equation:
(x + 40) + 52 = 180
→ x + 92 = 180
→ x = 88

✔ Check: 88 + 40 = 128; 128 + 52 = 180 → Correct!

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Final Answer:
x = 55, 8, 22, 16, 25, 17, 26, 88