Let’s solve each problem step by step. Remember:
the angles in any quadrilateral add up to 360°. For parallelograms, opposite angles are equal and adjacent angles add up to 180°.
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First Quadrilateral (orange)
Angles given: 67°, 90°, 90°
Missing angle = a
Add known angles:
67 + 90 + 90 = 247°
So, a = 360 - 247 =
113°
✔ Check: 67 + 90 + 90 + 113 = 360 → Correct!
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Second Quadrilateral (green)
Angles given: 90°, 117°, 74°
Missing angle = b
Add known angles:
90 + 117 + 74 = 281°
b = 360 - 281 =
79°
✔ Check: 90 + 117 + 74 + 79 = 360 → Correct!
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Third Quadrilateral (purple)
Angles given: 111°, 55°, 107°
Missing angle = c
Add known angles:
111 + 55 + 107 = 273°
c = 360 - 273 =
87°
✔ Check: 111 + 55 + 107 + 87 = 360 → Correct!
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Fourth Quadrilateral (pink)
Angles given: 47°, 89°, 82°
Missing angle = d
Add known angles:
47 + 89 + 82 = 218°
d = 360 - 218 =
142°
✔ Check: 47 + 89 + 82 + 142 = 360 → Correct!
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Fifth Shape (orange arrowhead — still a quadrilateral!)
Angles given: 79°, 38°, 27°
Missing angle = e
Add known angles:
79 + 38 + 27 = 144°
e = 360 - 144 =
216°
Wait — that seems big? But yes! In a concave quadrilateral (like an arrowhead), one angle can be greater than 180°. Let’s check:
79 + 38 + 27 + 216 = 360 → Correct!
✔ So e =
216°
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Sixth Shape (teal arrowhead)
Angles given: 48°, 239°, 34°
Missing angle = f
Add known angles:
48 + 239 + 34 = 321°
f = 360 - 321 =
39°
✔ Check: 48 + 239 + 34 + 39 = 360 → Correct!
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Parallelogram 1 (purple with markings)
Given: Two angles shown — 108° and 72°
In a parallelogram:
- Opposite angles are equal.
- Adjacent angles add to 180°.
Looking at the shape:
- The angle labeled “a” is opposite the 108° angle → so
a = 108°
- The angle labeled “b” is opposite the 72° angle → so
b = 72°
Also check: 108 + 72 = 180 → adjacent angles sum to 180 → correct for parallelogram.
✔ So: a =
108°, b =
72°
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Parallelogram 2 (purple with different markings)
Given: One angle = 57°
We need to find c, d, e.
In a parallelogram:
- Opposite angles are equal.
- Adjacent angles add to 180°.
Angle next to 57° is c → they are adjacent → c = 180 - 57 =
123°
Then:
- d is opposite 57° → d =
57°
- e is opposite c → e =
123°
Check: 57 + 123 + 57 + 123 = 360 → Correct!
✔ So: c =
123°, d =
57°, e =
123°
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Final Answer:
a = 113°
b = 79°
c = 87°
d = 142°
e = 216°
f = 39°
Parallelogram 1: a = 108°, b = 72°
Parallelogram 2: c = 123°, d = 57°, e = 123°
Parent Tip: Review the logic above to help your child master the concept of quadrilaterals angles worksheet.
