Find the missing angles in quadrilaterals with this math worksheet.

Let’s solve each problem one by one. Remember: the angles in any quadrilateral add up to 360°. We’ll use that rule for every question.

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Problem 1)
We have a quadrilateral with three known angles:
- One angle is 75°
- Two angles are right angles (marked with squares) → each is 90°

So, total of known angles = 75 + 90 + 90 = 255°
Missing angle = 360 - 255 = 105°

✔ Answer for 1): 105°

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Problem 2)
Known angles: 84°, 50°, 146°
Add them: 84 + 50 = 134; 134 + 146 = 280°
Missing angle = 360 - 280 = 80°

✔ Answer for 2): 80°

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Problem 3)
Known angles: 52°, 128°, 43°
Add them: 52 + 128 = 180; 180 + 43 = 223°
Missing angle = 360 - 223 = 137°

✔ Answer for 3): 137°

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Problem 4)
This is a parallelogram (opposite sides have arrows → parallel). In a parallelogram:
- Opposite angles are equal
- Adjacent angles add to 180°

Given one angle is 78°. The angle opposite it must also be 78°.
The other two angles are equal to each other and must add with 78° to make 180° (since adjacent angles in parallelogram are supplementary).

So, missing angle next to 78° = 180 - 78 = 102°
And the last angle (opposite that) is also 102°

But wait — let’s check using total sum too:
If we didn’t know it was a parallelogram, we’d say:
Three angles? Actually, only one is given: 78°. But since it's marked as a parallelogram, we can use properties.

Actually, looking at the diagram:
It shows two angles marked “?” and one 78°. Since opposite angles are equal, the angle opposite 78° is also 78°. Then the other two angles are equal and together must be 360 - 78 - 78 = 204°, so each is 102°.

So the two “?” angles are both 102°

✔ Answer for 4): Both ? = 102°

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Problem 5)
Two right angles (90° each), one angle is 67°
Sum of known: 90 + 90 + 67 = 247°
Missing angle = 360 - 247 = 113°

✔ Answer for 5): 113°

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Problem 6)
Known angles: 47°, 128°, 86°
Add them: 47 + 128 = 175; 175 + 86 = 261°
Missing angle = 360 - 261 = 99°

✔ Answer for 6): 99°

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Problem 7)
It says “A rhombus”. In a rhombus:
- All sides equal
- Opposite angles are equal
- Angles add to 360°

Given: two angles are 34°, one is 146°, and one is “?”

Since opposite angles are equal, the 34° angles are opposite each other. So the other two angles must be equal to each other.

Wait — actually, in the diagram, it shows:
- Top angle: 146°
- Left and right angles: 34° each
- Bottom angle: ?

In a rhombus, opposite angles are equal. So if top is 146°, bottom should also be 146°? But then left and right are 34° each.

Check sum: 146 + 146 + 34 + 34 = 360 → yes! That works.

But in the diagram, the bottom angle is marked “?”, and the top is 146°, left and right are 34°.

So the bottom angle must be equal to the top angle → 146°

Wait — but let me double-check: maybe the 146° is not opposite the “?”? Looking at the shape: it’s drawn like a diamond. Typically, top and bottom are opposite, left and right are opposite.

So if left and right are both 34°, they are opposite → good. Then top and bottom must be equal. Top is 146°, so bottom must be 146°.

But let’s verify with addition: 34 + 34 + 146 + ? = 360
→ 214 + ? = 360 → ? = 146°

Yes.

✔ Answer for 7): 146°

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Problem 8)
This is a tricky one — it looks like a concave quadrilateral (one angle is reflex, greater than 180°). The angle marked 234° is inside the shape? Wait — no, in standard geometry, when we say "angles in a quadrilateral", we mean the interior angles, even if one is reflex.

But note: the figure has an angle marked 234° — that’s likely the *reflex* interior angle. And another angle is 23°, and there’s a right angle (90°), and one “?”.

So known angles: 23°, 90°, 234°, and ?

Add known: 23 + 90 = 113; 113 + 234 = 347°

Then ? = 360 - 347 = 13°

Wait — is that possible? Let me think.

In some diagrams, especially concave ones, the large angle might be labeled as the exterior or something — but here it’s clearly marked inside the shape as 234°, which is valid for a concave quadrilateral.

Total must still be 360°.

So: 23 + 90 + 234 + ? = 360
→ 347 + ? = 360 → ? = 13°

That seems small, but mathematically correct.

Alternatively, sometimes people get confused and think the 234° is the outside angle — but the problem says “angles in a quadrilateral”, and the mark is on the inside, so we take it as interior.

Also, the right angle is marked with a square, so definitely 90°.

So yes, ? = 13°

✔ Answer for 8): 13°

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Final Answers:

1) 105°
2) 80°
3) 137°
4) Both ? = 102°
5) 113°
6) 99°
7) 146°
8) 13°

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Final Answer:
1) 105°
2) 80°
3) 137°
4) 102°, 102°
5) 113°
6) 99°
7) 146°
8) 13°