Angles in a Parallelogram Worksheets - Free Printable

Let’s solve each parallelogram problem one by one.

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.

---

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°

---

Problem 2:
Given angle = 50°

Opposite angles equal → so the angle opposite 50° is also 50°. That must be x.

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

z is opposite y → so z = 130°

Check: 50 + 130 + 50 + 130 = 360° ✔

→ x = 50°, y = 130°, z = 130°

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°

Then consecutive to 50° is y and z → both should be 130°? But wait — in a parallelogram, only two pairs of opposite angles.

Actually, if bottom right is 50°, then top left (x) = 50° (opposite).

Then top right (y) and bottom left (z) are the other pair → they must be equal to each other, and each adds with 50° to make 180° → so y = 130°, z = 130°.

Yes, that’s correct.

→ x = 50°, y = 130°, z = 130°

But hold on — in some diagrams, labels might be placed differently. Let me double-check standard labeling.

Typically, in such problems, the vertices are labeled clockwise or counter-clockwise.

Assuming standard labeling:

For problem 2:

- Bottom right = 50°
- So top left (x) = opposite = 50°
- Top right (y) = adjacent to 50° → 180 - 50 = 130°
- Bottom left (z) = opposite to y → 130°

Yes.

→ x = 50°, y = 130°, z = 130°

---

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

So:

Opposite angle (top left, x) = 121°

Adjacent angles (y and z) = 180 - 121 = 59°

And since y and z are opposite each other? Wait — let's see positions.

Diagram:

Top left: x
Top right: y
Bottom left: z
Bottom right: 121°

So:

x (top left) is opposite bottom right → x = 121°

y (top right) is adjacent to 121° → y = 180 - 121 = 59°

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

Check: 121 + 59 + 121 + 59 = 360° ✔

→ x = 121°, y = 59°, z = 59°

---

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

Positions:

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

So:

x (bottom left) is opposite top right (z)? No — opposite corners.

Actually:

Bottom right = 95° → its opposite is top left → so y = 95°

Then adjacent angles: x and z must each be 180 - 95 = 85°

And x and z are opposite each other? Let’s see:

If bottom right = 95°, then:

- Opposite: top left = y = 95°
- Adjacent: bottom left (x) and top right (z) → both should be 85°, and they are opposite each other → yes.

So x = 85°, z = 85°

Check: 95 + 85 + 95 + 85 = 360° ✔

→ x = 85°, y = 95°, z = 85°

---

Problem 5:
This is a parallelogram tilted. Given angle = 40° at top right.

Labels:

Top left: ?
Top right: 40°
Bottom left: x
Bottom right: y
Also, there’s a z near the diagonal? Wait — looking at the diagram description:

It says: “z” is marked near the diagonal, but actually in the text it says:

“5) [diagram] with angles labeled: top right = 40°, bottom left = x, bottom right = y, and z is another angle?”

Wait — re-examining the original problem statement from user input:

In problem 5, the diagram has:

- One angle given as 40° (probably top right)
- Angles labeled: x (bottom left), y (bottom right), z (maybe top left?)

Actually, based on typical layout:

Assume:

Top left: z
Top right: 40°
Bottom left: x
Bottom right: y

In parallelogram:

Opposite angles equal → so z (top left) = y (bottom right)

And x (bottom left) = 40° (top right) → because they are opposite? Wait no.

Standard: opposite corners.

If top right = 40°, then bottom left (x) is opposite → so x = 40°

Then top left (z) and bottom right (y) are the other pair → they are equal, and each = 180 - 40 = 140°

So z = 140°, y = 140°

Check: 40 + 140 + 40 + 140 = 360° ✔

→ x = 40°, y = 140°, z = 140°

But wait — in the problem, it says "z" is labeled — probably at top left.

Yes.

→ x = 40°, y = 140°, z = 140°

---

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

Labels:

Top left: 67°
Top right: y
Bottom left: x
Bottom right: z

So:

Top left = 67° → opposite is bottom right → z = 67°

Adjacent angles: top right (y) and bottom left (x) → each = 180 - 67 = 113°

And x and y are opposite? No — x (bottom left) and y (top right) are not opposite; actually, in parallelogram, opposite are:

Top left ↔ bottom right → 67° and z → z=67°

Top right ↔ bottom left → y and x → so x = y = 113°

Yes.

→ x = 113°, y = 113°, z = 67°

---

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

Labels:

Top left: y
Top right: 73°
Bottom left: x
Bottom right: z

So:

Top right = 73° → opposite is bottom left → x = 73°

Then top left (y) and bottom right (z) are the other pair → each = 180 - 73 = 107°

And y and z are opposite → so y = z = 107°

→ x = 73°, y = 107°, z = 107°

---

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

Labels:

Top left: z
Top right: x
Bottom left: 123°
Bottom right: y

So:

Bottom left = 123° → opposite is top right → x = 123°

Adjacent angles: top left (z) and bottom right (y) → each = 180 - 123 = 57°

And z and y are opposite → so z = y = 57°

→ x = 123°, y = 57°, z = 57°

---

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

Labels:

Top left: y
Top right: z
Bottom left: x
Bottom right: 93°

So:

Bottom right = 93° → opposite is top left → y = 93°

Adjacent angles: bottom left (x) and top right (z) → each = 180 - 93 = 87°

And x and z are opposite → so x = z = 87°

→ x = 87°, y = 93°, z = 87°

---

Now, compiling all answers:

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°

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°