Worksheet for finding missing angles in parallelograms.

Let's solve each of these parallelogram angle problems step by step. We'll use the properties of a parallelogram:

🔷 Properties of a Parallelogram:

1. Opposite angles are equal.
2. Adjacent angles are supplementary (add up to 180°).
3. Opposite sides are parallel and equal.

We will use these properties to find the missing angles.

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1)

Given: One angle = 115°

- Since opposite angles are equal:
- $ x = 115^\circ $
- $ y = 115^\circ $ (opposite to x)
- Adjacent angles add to 180°:
- $ z = 180^\circ - 115^\circ = 65^\circ $
- So, $ z = 65^\circ $

✔ Answer:
- $ x = 115^\circ $
- $ y = 115^\circ $
- $ z = 65^\circ $

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2)

Given: One angle = 50°

- Opposite angles are equal:
- $ x = 50^\circ $
- $ y = 50^\circ $
- Adjacent angles sum to 180°:
- $ z = 180^\circ - 50^\circ = 130^\circ $

✔ Answer:
- $ x = 50^\circ $
- $ y = 50^\circ $
- $ z = 130^\circ $

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3)

Given: One angle = 121°

- Opposite angles are equal:
- $ x = 121^\circ $
- $ y = 121^\circ $
- Adjacent angles sum to 180°:
- $ z = 180^\circ - 121^\circ = 59^\circ $

✔ Answer:
- $ x = 121^\circ $
- $ y = 121^\circ $
- $ z = 59^\circ $

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4)

Given: One angle = 95°

- Opposite angles are equal:
- $ x = 95^\circ $
- $ y = 95^\circ $
- Adjacent angles sum to 180°:
- $ z = 180^\circ - 95^\circ = 85^\circ $

✔ Answer:
- $ x = 95^\circ $
- $ y = 95^\circ $
- $ z = 85^\circ $

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5)

Given: One angle = 40°

- Opposite angles are equal:
- $ x = 40^\circ $
- $ y = 40^\circ $
- Adjacent angles sum to 180°:
- $ z = 180^\circ - 40^\circ = 140^\circ $

✔ Answer:
- $ x = 40^\circ $
- $ y = 40^\circ $
- $ z = 140^\circ $

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6)

Given: One angle = 67°

- Opposite angles are equal:
- $ x = 67^\circ $
- $ y = 67^\circ $
- Adjacent angles sum to 180°:
- $ z = 180^\circ - 67^\circ = 113^\circ $

✔ Answer:
- $ x = 67^\circ $
- $ y = 67^\circ $
- $ z = 113^\circ $

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7)

Given: One angle = 74°

- Opposite angles are equal:
- $ x = 74^\circ $
- $ y = 74^\circ $
- Adjacent angles sum to 180°:
- $ z = 180^\circ - 74^\circ = 106^\circ $

✔ Answer:
- $ x = 74^\circ $
- $ y = 74^\circ $
- $ z = 106^\circ $

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8)

Given: One angle = 133°

- Opposite angles are equal:
- $ x = 133^\circ $
- $ y = 133^\circ $
- Adjacent angles sum to 180°:
- $ z = 180^\circ - 133^\circ = 47^\circ $

✔ Answer:
- $ x = 133^\circ $
- $ y = 133^\circ $
- $ z = 47^\circ $

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9)

Given: One angle = 93°

- Opposite angles are equal:
- $ x = 93^\circ $
- $ y = 93^\circ $
- Adjacent angles sum to 180°:
- $ z = 180^\circ - 93^\circ = 87^\circ $

✔ Answer:
- $ x = 93^\circ $
- $ y = 93^\circ $
- $ z = 87^\circ $

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✔ Final Answers Summary:

| Problem | x | y | z |
|--------|---------|---------|---------|
| 1 | 115° | 115° | 65° |
| 2 | 50° | 50° | 130° |
| 3 | 121° | 121° | 59° |
| 4 | 95° | 95° | 85° |
| 5 | 40° | 40° | 140° |
| 6 | 67° | 67° | 113° |
| 7 | 74° | 74° | 106° |
| 8 | 133° | 133° | 47° |
| 9 | 93° | 93° | 87° |

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📌 Key Takeaway:

In every parallelogram:
- Opposite angles are equal.
- Adjacent angles are supplementary (sum to 180°).

Use these two rules to solve any angle problem in a parallelogram!