Find the missing angles in each parallelogram.

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

🔷 Properties of Parallelograms:

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

We’ll label the angles as shown in the diagrams and apply these rules.

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1)

Given: One angle = 115°

- Opposite angles are equal → $ y = 115^\circ $
- Adjacent angles are supplementary → $ x = 180^\circ - 115^\circ = 65^\circ $
- Since opposite angles are equal → $ z = x = 65^\circ $

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

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2)

Given: One angle = 50°

- Opposite angles are equal → $ y = 50^\circ $
- Adjacent angles are supplementary → $ x = 180^\circ - 50^\circ = 130^\circ $
- $ z = x = 130^\circ $

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

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3)

Given: One angle = 121°

- Opposite angles are equal → $ y = 121^\circ $
- Adjacent angles are supplementary → $ x = 180^\circ - 121^\circ = 59^\circ $
- $ z = x = 59^\circ $

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

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4)

Given: One angle = 95°

- Opposite angles are equal → $ y = 95^\circ $
- Adjacent angles are supplementary → $ x = 180^\circ - 95^\circ = 85^\circ $
- $ z = x = 85^\circ $

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

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5)

Given: One angle = 40°, and another angle labeled as $ z $

Note: The diagram shows a 40° angle and an angle labeled $ z $. Since it’s a parallelogram, adjacent angles are supplementary.

Assume the 40° is one angle → then its adjacent angle $ z = 180^\circ - 40^\circ = 140^\circ $

Then:
- $ x = $ opposite of $ z $ → $ x = 140^\circ $
- $ y = $ opposite of 40° → $ y = 40^\circ $

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

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6)

Given: One angle = 67°

- Opposite angles are equal → $ y = 67^\circ $
- Adjacent angles are supplementary → $ x = 180^\circ - 67^\circ = 113^\circ $
- $ z = x = 113^\circ $

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

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7)

Given: One angle = 71°

- Opposite angles are equal → $ y = 71^\circ $
- Adjacent angles are supplementary → $ x = 180^\circ - 71^\circ = 109^\circ $
- $ z = x = 109^\circ $

✔ So:
- $ x = 109^\circ $
- $ y = 71^\circ $
- $ z = 109^\circ $

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8)

Given: One angle = 133°

- Opposite angles are equal → $ y = 133^\circ $
- Adjacent angles are supplementary → $ x = 180^\circ - 133^\circ = 47^\circ $
- $ z = x = 47^\circ $

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

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9)

Given: One angle = 94°

- Opposite angles are equal → $ y = 94^\circ $
- Adjacent angles are supplementary → $ x = 180^\circ - 94^\circ = 86^\circ $
- $ z = x = 86^\circ $

✔ So:
- $ x = 86^\circ $
- $ y = 94^\circ $
- $ z = 86^\circ $

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✔ Final Answers:

| Problem | x | y | z |
|--------|---------|---------|---------|
| 1) | 65° | 115° | 65° |
| 2) | 130° | 50° | 130° |
| 3) | 59° | 121° | 59° |
| 4) | 85° | 95° | 85° |
| 5) | 140° | 40° | 140° |
| 6) | 113° | 67° | 113° |
| 7) | 109° | 71° | 109° |
| 8) | 47° | 133° | 47° |
| 9) | 86° | 94° | 86° |

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📝 Summary:

All solutions use:
- Opposite angles = Equal
- Adjacent angles = Supplementary (sum to 180°)

These two properties are enough to find all missing angles in any parallelogram.

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