Angles in a Parallelogram Worksheets - Free Printable

Let’s solve each parallelogram problem step by step.

Remember these key rules for angles in a parallelogram:
- Opposite angles are equal.
- Consecutive (next to each other) angles add up to 180°.
- The sum of all four angles is always 360°.

We’ll use these rules to find x, y, and z in each case.

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Problem 1:
Given angle = 115°

In a parallelogram:
- Opposite angles are equal → so the angle opposite 115° is also 115°. That must be y.
- Consecutive angles add to 180° → so x + 115° = 180° → x = 65°
- Then z is opposite x → so z = 65°

Check: 115 + 65 + 115 + 65 = 360° ✔

→ x = 65°, y = 115°, z = 65°

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Problem 2:
Given angle = 50°

Opposite angles equal → so the angle opposite 50° is also 50°. That’s z.

Consecutive angles add to 180° → so y + 50° = 180° → y = 130°

Then x is opposite y → x = 130°

Check: 130 + 50 + 130 + 50 = 360° ✔

→ x = 130°, y = 130°, z = 50°

Wait — let’s look at the diagram again. In problem 2, the labeled angles are:

Top left: x
Top right: y
Bottom left: z
Bottom right: 50°

So bottom right = 50° → then top left (x) is opposite → x = 50°? No! Wait — in a parallelogram, opposite corners are equal.

Actually, in standard labeling:

If bottom right is 50°, then top left (x) is opposite → x = 50°

Then consecutive angle to 50° is y (top right) → y + 50° = 180° → y = 130°

Then z (bottom left) is opposite y → z = 130°

Yes, that makes sense.

→ x = 50°, y = 130°, z = 130°

But wait — let me double-check with the shape. If it's slanted like a typical parallelogram, and 50° is at bottom right, then yes, opposite is top left = x = 50°. Adjacent angles are supplementary.

So correction:

→ x = 50°, y = 130°, z = 130°

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Problem 3:
Given angle = 121° at bottom right.

Opposite angle is top left → that’s x → so x = 121°

Consecutive angle to 121° is y (top right) → y + 121° = 180° → y = 59°

Then z (bottom left) is opposite y → z = 59°

Check: 121 + 59 + 121 + 59 = 360° ✔

→ x = 121°, y = 59°, z = 59°

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Problem 4:
Given angle = 95° at bottom right.

Opposite angle is top left → that’s x → x = 95°

Consecutive angle to 95° is y (top left? Wait — let’s label properly).

Diagram shows:

Top left: y
Top right: z
Bottom left: x
Bottom right: 95°

So bottom right = 95° → opposite is top left → y = 95°

Then consecutive to 95° is x (bottom left) → x + 95° = 180° → x = 85°

Then z (top right) is opposite x → z = 85°

Check: 85 + 95 + 85 + 95 = 360° ✔

→ x = 85°, y = 95°, z = 85°

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Problem 5:
Given angle = 40° at top right.

Opposite angle is bottom left → that’s x → x = 40°

Consecutive angle to 40° is y (bottom right) → y + 40° = 180° → y = 140°

Then z (top left) is opposite y → z = 140°

Check: 40 + 140 + 40 + 140 = 360° ✔

→ x = 40°, y = 140°, z = 140°

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Problem 6:
Given angle = 67° at top left.

Opposite angle is bottom right → that’s z → z = 67°

Consecutive angle to 67° is y (top right) → y + 67° = 180° → y = 113°

Then x (bottom left) is opposite y → x = 113°

Check: 113 + 113 + 67 + 67 = 360° ✔

→ x = 113°, y = 113°, z = 67°

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Problem 7:
Given angle = 73° at top right.

Opposite angle is bottom left → that’s x → x = 73°

Consecutive angle to 73° is y (top left) → y + 73° = 180° → y = 107°

Then z (bottom right) is opposite y → z = 107°

Check: 73 + 107 + 73 + 107 = 360° ✔

→ x = 73°, y = 107°, z = 107°

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Problem 8:
Given angle = 123° at bottom left.

Opposite angle is top right → that’s x → x = 123°

Consecutive angle to 123° is y (bottom right) → y + 123° = 180° → y = 57°

Then z (top left) is opposite y → z = 57°

Check: 123 + 57 + 123 + 57 = 360° ✔

→ x = 123°, y = 57°, z = 57°

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Problem 9:
Given angle = 93° at bottom right.

Opposite angle is top left → that’s y → y = 93°

Consecutive angle to 93° is x (bottom left) → x + 93° = 180° → x = 87°

Then z (top right) is opposite x → z = 87°

Check: 87 + 93 + 87 + 93 = 360° ✔

→ x = 87°, y = 93°, z = 87°

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Now let’s compile all answers clearly:

Final Answer:
1) x = 65°, y = 115°, z = 65°
2) x = 50°, y = 130°, z = 130°
3) x = 121°, y = 59°, z = 59°
4) x = 85°, y = 95°, z = 85°
5) x = 40°, y = 140°, z = 140°
6) x = 113°, y = 113°, z = 67°
7) x = 73°, y = 107°, z = 107°
8) x = 123°, y = 57°, z = 57°
9) x = 87°, y = 93°, z = 87°