Angles Worksheets | Geometry worksheets, Math, Angles worksheet - Free Printable

To solve each problem, we use the Linear Pair Theorem, which states:

> If two angles form a linear pair (i.e., they are adjacent and their non-common sides form a straight line), then they are supplementary — meaning their measures add up to 180°.

So for each diagram, we set up the equation:

> Angle 1 + Angle 2 = 180°

Then solve for `x`.

---

Problem 1 (Top Left)

Angles: `2x + 5` and `65°`

Equation:
```
(2x + 5) + 65 = 180
2x + 70 = 180
2x = 110
x = 55
```

✔ Answer: x = 55

---

Problem 2 (Top Right)

Angles: `136°` and `4x + 12`

Equation:
```
136 + (4x + 12) = 180
4x + 148 = 180
4x = 32
x = 8
```

✔ Answer: x = 8

---

Problem 3 (Middle Left)

Angles: `45°` and `5x + 25`

Equation:
```
45 + (5x + 25) = 180
5x + 70 = 180
5x = 110
x = 22
```

✔ Answer: x = 22

---

Problem 4 (Middle Right)

Angles: `7x - 8` and `76°`

Equation:
```
(7x - 8) + 76 = 180
7x + 68 = 180
7x = 112
x = 16
```

✔ Answer: x = 16

---

Problem 5 (Bottom Left)

Angles: `3x - 17` and `122°`

Equation:
```
(3x - 17) + 122 = 180
3x + 105 = 180
3x = 75
x = 25
```

✔ Answer: x = 25

---

Problem 6 (Bottom Right, First Row)

Angles: `80°` and `8x - 36`

Equation:
```
80 + (8x - 36) = 180
8x + 44 = 180
8x = 136
x = 17
```

✔ Answer: x = 17

---

Problem 7 (Bottom Left, Second Row)

Angles: `4x - 30` and `106°`

Equation:
```
(4x - 30) + 106 = 180
4x + 76 = 180
4x = 104
x = 26
```

✔ Answer: x = 26

---

Problem 8 (Bottom Right, Second Row)

Angles: `x + 40` and `52°`

Equation:
```
(x + 40) + 52 = 180
x + 92 = 180
x = 88
```

✔ Answer: x = 88

---

## ✔ Final Answers:

| Problem | x |
|---------|-------|
| 1 | 55 |
| 2 | 8 |
| 3 | 22 |
| 4 | 16 |
| 5 | 25 |
| 6 | 17 |
| 7 | 26 |
| 8 | 88 |

You can now fill in the boxes on your worksheet with these values!