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 shape.
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Problem 1)
We have a quadrilateral with three known angles:
- One angle is 75°
- Two angles are right angles (90° each) — shown by the little squares
So, total of known angles = 75 + 90 + 90 =
255°
Missing angle = 360 - 255 =
105°
✔ Answer for #1:
105°
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Problem 2)
Angles given: 84°, 50°, 146°
Add them: 84 + 50 + 146 =
280°
Missing angle = 360 - 280 =
80°
✔ Answer for #2:
80°
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Problem 3)
Angles given: 52°, 128°, 43°
Add them: 52 + 128 + 43 =
223°
Missing angle = 360 - 223 =
137°
✔ Answer for #3:
137°
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Problem 4)
This is a parallelogram (opposite sides parallel). In a parallelogram:
- Opposite angles are equal
- Adjacent angles add to 180°
Given: one angle is 78°
→ The opposite angle is also
78°
→ The other two angles must be equal and each = 180 - 78 =
102°
Check: 78 + 78 + 102 + 102 = 360 → ✔️
✔ Answers for #4: Top left =
102°, top right =
102°, bottom right =
78°
Wait — let’s look at the diagram again. The question marks are on:
- Top left (?)
- Top right (?)
- Bottom right (?)
Bottom left is 78°. So:
Top left = opposite of bottom right? Actually, in a parallelogram, opposite angles are equal.
If bottom left is 78°, then top right is also 78°.
Then the other two (top left and bottom right) are equal and each = (360 - 78 - 78)/2 = 204/2 =
102°
So:
Top left ? =
102°
Top right ? =
78°
Bottom right ? =
102°
But wait — looking at the arrows: it's a parallelogram, so yes.
Actually, let me label positions:
Assume vertices go clockwise:
Bottom left = 78°
Bottom right = ?
Top right = ?
Top left = ?
In parallelogram:
Opposite angles equal → bottom left = top right = 78°
Adjacent angles sum to 180° → bottom left + bottom right = 180 → bottom right = 102°
Then top left = bottom right = 102°
So:
Top left ? =
102°
Top right ? =
78°
Bottom right ? =
102°
✔ Final for #4:
Top left:
102°
Top right:
78°
Bottom right:
102°
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Problem 5)
Two right angles (90° each), one angle 67°
Known angles: 90 + 90 + 67 =
247°
Missing angle = 360 - 247 =
113°
✔ Answer for #5:
113°
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Problem 6)
Angles given: 47°, 128°, 86°
Add them: 47 + 128 + 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 equal
- Angles add to 360°
Given: two angles are 34°, one is 146°
Since opposite angles are equal, the missing angle must be opposite the 146° angle → so it should also be
146°
Check: 34 + 34 + 146 + 146 = 360 → ✔️
✔ Answer for #7:
146°
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Problem 8)
This is a concave quadrilateral (one angle > 180°). But still, all four interior angles add to 360°.
Given angles:
- 23°
- 234° (this is the reflex angle inside — but we treat it as an interior angle)
- Right angle (90°) — shown by square
- Missing angle ?
Add known: 23 + 234 + 90 =
347°
Missing angle = 360 - 347 =
13°
✔ Answer for #8:
13°
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Final Answer:
1) 105°
2) 80°
3) 137°
4) Top left: 102°, Top right: 78°, Bottom right: 102°
5) 113°
6) 99°
7) 146°
8) 13°
Parent Tip: Review the logic above to help your child master the concept of geometry quadrilaterals worksheet.
