Worksheet for finding missing angles in quadrilaterals, including examples and practice problems.

We are given a worksheet titled “Finding the Missing Angles in a Quadrilateral”. The key concept is:

> The sum of the interior angles of any quadrilateral is always 360°.

We will use this rule to find each missing angle `x°` (and in problem 7, also `y°`).

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Problem 1:

Angles: 154°, 26°, 154°, x°
Sum = 154 + 26 + 154 + x = 360
→ 334 + x = 360
→ x = 26°

✔ Answer: 26°

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Problem 2:

Angles: x°, 82°, 88°, 77°
Sum = x + 82 + 88 + 77 = 360
→ x + 247 = 360
→ x = 113°

✔ Answer: 113°

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Problem 3:

Angles: 38°, 54°, 148°, x°
Sum = 38 + 54 + 148 + x = 360
→ 240 + x = 360
→ x = 120°

✔ Answer: 120°

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Problem 4:

Angles: 120°, 66°, 60°, x°
Sum = 120 + 66 + 60 + x = 360
→ 246 + x = 360
→ x = 114°

✔ Answer: 114°

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Problem 5:

Angles: x°, 150°, 66°, 100°
Sum = x + 150 + 66 + 100 = 360
→ x + 316 = 360
→ x = 44°

✔ Answer: 44°

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Problem 6:

This is a trapezoid with two right angles (marked with squares). So two angles are 90° each.
Given: 90°, 90°, 67°, x°
Sum = 90 + 90 + 67 + x = 360
→ 247 + x = 360
→ x = 113°

✔ Answer: 113°

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Problem 7:

This one has an exterior angle marked as 348°. We need to find `x°` and `y°`.

First, recall:
> Interior angle + Exterior angle = 360° (they form a full circle at that vertex)

So, the interior angle at the bottom-right corner is:
360° - 348° = 12°

Now, we have a quadrilateral with angles: x°, 90° (right angle), y°, and 12°.

Wait — actually, looking at the diagram, there are two right angles (squares) at top-left and bottom-left. So angles are:

- Top-left: 90°
- Bottom-left: 90°
- Bottom-right: 12° (interior, from exterior 348°)
- Top-right: x°
- And bottom side has angle labeled y° — which must be the bottom-right interior angle, but we just calculated it as 12°? That doesn’t match.

Let’s re-express:

Actually, the diagram shows:

- Top-left: right angle → 90°
- Bottom-left: right angle → 90°
- Top-right: x°
- Bottom-right: labeled y°, but with an exterior angle of 348° drawn around it.

So, the interior angle at bottom-right is y°, and since the exterior angle is 348°, then:

> y° + 348° = 360° → y° = 12°

Now, sum of all interior angles = 360°

So: 90° (top-left) + 90° (bottom-left) + x° (top-right) + y° (bottom-right) = 360°
→ 90 + 90 + x + 12 = 360
→ 192 + x = 360
→ x = 168°

✔ Answer: x° = 168°, y° = 12°

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Problem 8:

Angles: x°, 58°, 58°, 122°
Sum = x + 58 + 58 + 122 = 360
→ x + 238 = 360
→ x = 122°

✔ Answer: 122°

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## ✔ Final Answers:

1. 26°
2. 113°
3. 120°
4. 114°
5. 44°
6. 113°
7. x° = 168°, y° = 12°
8. 122°

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📝 Summary:

All problems rely on the fundamental property:
> Sum of interior angles in any quadrilateral = 360°

For Problem 7, we also used the fact that an interior angle and its adjacent exterior angle add up to 360°.

You can now confidently solve any similar quadrilateral angle problem!