Let’s solve each part step by step. Remember:
the sum of interior angles in any quadrilateral is always 360°. We’ll use that for all parts (a) through (i).
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(a)
Angles given: 155°, 50°, 55°, and x
Add the known angles:
155 + 50 + 55 = 260°
So, x = 360 - 260 =
100°
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(b)
Angles given: 70°, 50°, a right angle (90°), and x
Add them: 70 + 50 + 90 = 210°
x = 360 - 210 =
150°
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(c)
Angles given: 85°, 70°, 45°, and x
Add: 85 + 70 + 45 = 200°
x = 360 - 200 =
160°
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(d)
Angles given: 97°, 86°, 114°, and x
Add: 97 + 86 + 114 = 297°
x = 360 - 297 =
63°
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(e)
This one looks tricky — it’s a concave quadrilateral (one angle “dents” inward). But the rule still holds: total = 360°.
Given angles: 77°, 40°, 212°, and x
Wait — 212°? That’s the reflex angle inside the shape. In quadrilaterals, we usually add the *interior* angles as they are drawn — even if one is greater than 180°. So yes, include 212°.
Add: 77 + 40 + 212 = 329°
x = 360 - 329 =
31°
*(Note: Sometimes students get confused with reflex angles — but since the diagram shows 212° as an interior angle, we treat it as such.)*
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(f)
It’s a trapezoid with two right angles (90° each), one angle is 52°, and another is x. Also, top and bottom sides are parallel (marked with arrows).
But again, just use total = 360°.
Angles: 90°, 90°, 52°, x
Add: 90 + 90 + 52 = 232°
x = 360 - 232 =
128°
*(Alternatively, since it’s a trapezoid with parallel sides, consecutive angles between parallels are supplementary — so 52° + x = 180° → x = 128°. Same answer!)*
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(g)
Angles given: 88°, 142°, 106°, and x
Add: 88 + 142 + 106 = 336°
x = 360 - 336 =
24°
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(h)
Trapezoid again (top and bottom parallel). Angles: 115°, 139°, 41°, and x
Total must be 360°.
Add: 115 + 139 + 41 = 295°
x = 360 - 295 =
65°
*(Check: Since top and bottom are parallel, left side angles should add to 180°? 115 + 65 = 180 ✔️. Right side: 139 + 41 = 180 ✔️. Perfect.)*
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(i)
Angles given: 76°, 135°, 81°, and x
Add: 76 + 135 + 81 = 292°
x = 360 - 292 =
68°
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Final Answer:
(a) 100°
(b) 150°
(c) 160°
(d) 63°
(e) 31°
(f) 128°
(g) 24°
(h) 65°
(i) 68°
Parent Tip: Review the logic above to help your child master the concept of angles in a quadrilateral worksheet.
