EduSahara™ Assignment
Name : Quadrilateral Angle Properties
Chapter : Quadrilaterals
Grade : ICSE Grade VII
License : Non Commercial Use
Question 1
1.
In parallelogram ABCD, if ∠D = 159.08°, then find the value of ∠B
  • (i)
    158.08°
  • (ii)
    157.08°
  • (iii)
    159.08°
  • (iv)
    161.08°
  • (v)
    160.08°
Question 2
2.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
  • (i)
    89°
  • (ii)
    91°
  • (iii)
    88°
  • (iv)
    90°
  • (v)
    92°
Question 3
3.
The sum of the interior angles of a quadrilateral is
  • (i)
    180°
  • (ii)
    90°
  • (iii)
    360°
  • (iv)
    270°
Question 4
4.
If ABCD is an isosceles trapezium, ∠A =
  • (i)
    90°
  • (ii)
    ∠D
  • (iii)
    ∠B
  • (iv)
    ∠C
Question 5
5.
ABCD is a rhombus in which ∠A = 120° .
 

BD
 
 
is the diagonal. Then △ABC is
  • (i)
    an obtuse angled triangle
  • (ii)
    an isosceles triangle
  • (iii)
    an equilateral triangle
  • (iv)
    None of these
  • (v)
    a scalene triangle
Question 6
6.
JKLM is a rhombus in which ∠J = 138° .
 

KM
 
 
is the diagonal. Then △JKL is
  • (i)
    an equilateral triangle
  • (ii)
    an isosceles triangle
  • (iii)
    an obtuse angled triangle
  • (iv)
    None of these
  • (v)
    a scalene triangle
Question 7
7.
The angles of a quadrilateral EFGH are in the ratio 6 : 5 : 7 : 22. Find the measure of each angle of the quadrilateral.
  • (i)
    E
    =
    56°
    ,
    F
    =
    44°
    ,
    G
    =
    61°
    ,
    H
    =
    199°
  • (ii)
    E
    =
    55°
    ,
    F
    =
    44°
    ,
    G
    =
    65°
    ,
    H
    =
    196°
  • (iii)
    E
    =
    54°
    ,
    F
    =
    45°
    ,
    G
    =
    63°
    ,
    H
    =
    198°
  • (iv)
    E
    =
    52°
    ,
    F
    =
    47°
    ,
    G
    =
    62°
    ,
    H
    =
    199°
  • (v)
    E
    =
    53°
    ,
    F
    =
    43°
    ,
    G
    =
    64°
    ,
    H
    =
    200°
Question 8
8.
Two adjacent angles of a parallelogram EFGH are in the ratio 26 : 34. Find the measure of each of its angles.
  • (i)
    E
    =
    78°
    ,
    F
    =
    102°
    ,
    G
    =
    78°
    ,
    H
    =
    102°
  • (ii)
    E
    =
    80°
    ,
    F
    =
    101°
    ,
    G
    =
    76°
    ,
    H
    =
    103°
  • (iii)
    E
    =
    76°
    ,
    F
    =
    104°
    ,
    G
    =
    77°
    ,
    H
    =
    103°
  • (iv)
    E
    =
    77°
    ,
    F
    =
    100°
    ,
    G
    =
    79°
    ,
    H
    =
    104°
  • (v)
    E
    =
    79°
    ,
    F
    =
    101°
    ,
    G
    =
    80°
    ,
    H
    =
    100°
Question 9
9.
    • In the adjoining figure,
    • PQRS
    • is a parallelogram in which
    • ∠SPR = 27.64°
    • ,
    • ∠RPQ = 23.88°
    • ,
    • ∠STR = 98.7°
    • . Calculate
    • ∠PQS
  • (i)
    58.42°
  • (ii)
    57.42°
  • (iii)
    59.42°
  • (iv)
    56.42°
  • (v)
    55.42°
Question 10
10.
    • In the adjoining figure,
    • JKLM
    • is a parallelogram in which
    • ∠MJL = 15.6°
    • ,
    • ∠LJK = 8.63°
    • ,
    • ∠MNL = 143.92°
    • . Calculate
    • ∠LMK
  • (i)
    26.45°
  • (ii)
    28.45°
  • (iii)
    27.45°
  • (iv)
    25.45°
  • (v)
    29.45°
Question 11
11.
    • In the adjoining figure,
    • CDEF
    • is a parallelogram in which
    • ∠FCE = 9.18°
    • ,
    • ∠ECD = 17.79°
    • ,
    • ∠FGE = 33.19°
    • . Calculate
    • ∠DEC
  • (i)
    9.18°
  • (ii)
    7.18°
  • (iii)
    11.18°
  • (iv)
    10.18°
  • (v)
    8.18°
Question 12
12.
    • In the adjoining figure,
    • DEFG
    • is a parallelogram in which
    • ∠GDF = 46.58°
    • ,
    • ∠FDE = 52.79°
    • ,
    • ∠GHF = 83.71°
    • . Calculate
    • ∠GEF
  • (i)
    35.12°
  • (ii)
    39.12°
  • (iii)
    37.12°
  • (iv)
    36.12°
  • (v)
    38.12°
Question 13
13.
    • In the adjoining figure,
    • NOPQ
    • is a rectangle.
    • If
    • ∠PNO = 40.36°
    • , find
    • ∠NOQ
  • (i)
    41.36°
  • (ii)
    39.36°
  • (iii)
    42.36°
  • (iv)
    38.36°
  • (v)
    40.36°
Question 14
14.
Three angles of quadrilateral measure 41.8°, 80.94° and 127.38° respectively. Find the measure of the fourth angle
  • (i)
    110.88°
  • (ii)
    111.88°
  • (iii)
    107.88°
  • (iv)
    108.88°
  • (v)
    109.88°
Question 15
15.
Three angles of a quadrilateral are equal and the fourth angle measure 55.83°. What is the measure of each of the equal angles?
  • (i)
    101.39°
  • (ii)
    99.39°
  • (iii)
    103.39°
  • (iv)
    102.39°
  • (v)
    100.39°
Question 16
16.
Two angles of a quadrilateral are of measure 73.69° and 90.69° respectively and the other two angles are equal. Find the measure of each of the equal angles.
  • (i)
    99.81°
  • (ii)
    97.81°
  • (iii)
    96.81°
  • (iv)
    95.81°
  • (v)
    98.81°
Question 17
17.
A quadrilateral has three acute angles, each measuring 76°. What is the measure of its fourth angle?
  • (i)
    131.00°
  • (ii)
    134.00°
  • (iii)
    130.00°
  • (iv)
    132.00°
  • (v)
    133.00°
Question 18
18.
    • One angle of a parallelogram measures
    • J
    • =
    • 71.79°
    • .
    • Find the measure of each of its remaining angles.
  • (i)
    K
    =
    110.21°
    ,
    L
    =
    73.79°
    ,
    M
    =
    110.21°
  • (ii)
    K
    =
    108.21°
    ,
    L
    =
    71.79°
    ,
    M
    =
    108.21°
  • (iii)
    K
    =
    109.21°
    ,
    L
    =
    72.79°
    ,
    M
    =
    109.21°
  • (iv)
    K
    =
    107.21°
    ,
    L
    =
    70.79°
    ,
    M
    =
    107.21°
  • (v)
    K
    =
    106.21°
    ,
    L
    =
    69.79°
    ,
    M
    =
    106.21°
Question 19
19.
    • Two adjacent angles of a parallelogram are in the ratio
    • 2 : 88
    • .
    • Find the measure of each of its angles.
  • (i)
    A
    =
    5°
    ,
    B
    =
    175°
    ,
    C
    =
    6°
    ,
    D
    =
    174°
  • (ii)
    A
    =
    4°
    ,
    B
    =
    176°
    ,
    C
    =
    4°
    ,
    D
    =
    176°
  • (iii)
    A
    =
    6°
    ,
    B
    =
    175°
    ,
    C
    =
    2°
    ,
    D
    =
    177°
  • (iv)
    A
    =
    3°
    ,
    B
    =
    174°
    ,
    C
    =
    5°
    ,
    D
    =
    178°
  • (v)
    A
    =
    2°
    ,
    B
    =
    178°
    ,
    C
    =
    3°
    ,
    D
    =
    177°
Question 20
20.
    • In the figure given below,
    • DEFG
    • is a rectangle.
    • Find the values of x and y
  • (i)
    x
    =
    28.81°
    ,
    y
    =
    57.62°
  • (ii)
    x
    =
    30.81°
    ,
    y
    =
    59.62°
  • (iii)
    x
    =
    26.81°
    ,
    y
    =
    55.62°
  • (iv)
    x
    =
    27.81°
    ,
    y
    =
    56.62°
  • (v)
    x
    =
    29.81°
    ,
    y
    =
    58.62°
Question 21
21.
    • In the figure given below,
    • MNOP
    • is a rectangle.
    • Find the values of x and y
  • (i)
    x
    =
    64.24°
    ,
    y
    =
    29.76°
  • (ii)
    x
    =
    61.24°
    ,
    y
    =
    26.76°
  • (iii)
    x
    =
    60.24°
    ,
    y
    =
    25.76°
  • (iv)
    x
    =
    62.24°
    ,
    y
    =
    27.76°
  • (v)
    x
    =
    63.24°
    ,
    y
    =
    28.76°
Question 22
22.
    • In the figure given below,
    • JKLM
    • is a rhombus.
    • Find the values of x and y
  • (i)
    x
    =
    21.15°
    ,
    y
    =
    21.15°
  • (ii)
    x
    =
    20.15°
    ,
    y
    =
    20.15°
  • (iii)
    x
    =
    23.15°
    ,
    y
    =
    23.15°
  • (iv)
    x
    =
    22.15°
    ,
    y
    =
    22.15°
  • (v)
    x
    =
    19.15°
    ,
    y
    =
    19.15°
Question 23
23.
    • In the figure given below,
    • FGHI
    • is a rhombus.
    • Find the values of x and y
  • (i)
    x
    =
    56.22°
    ,
    y
    =
    56.22°
  • (ii)
    x
    =
    60.22°
    ,
    y
    =
    60.22°
  • (iii)
    x
    =
    58.22°
    ,
    y
    =
    58.22°
  • (iv)
    x
    =
    57.22°
    ,
    y
    =
    57.22°
  • (v)
    x
    =
    59.22°
    ,
    y
    =
    59.22°
Question 24
24.
    • In the figure given below,
    • EFGH
    • is a rhombus.
    • Find the values of x and y
  • (i)
    x
    =
    53.67°
    ,
    y
    =
    34.33°
  • (ii)
    x
    =
    55.67°
    ,
    y
    =
    36.33°
  • (iii)
    x
    =
    56.67°
    ,
    y
    =
    37.33°
  • (iv)
    x
    =
    54.67°
    ,
    y
    =
    35.33°
  • (v)
    x
    =
    52.67°
    ,
    y
    =
    33.33°
Question 25
25.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
  • (i)
    J
    =
    61°
    ,
    K
    =
    119°
    ,
    L
    =
    62°
    ,
    M
    =
    118°
  • (ii)
    J
    =
    58°
    ,
    K
    =
    122°
    ,
    L
    =
    59°
    ,
    M
    =
    121°
  • (iii)
    J
    =
    60°
    ,
    K
    =
    120°
    ,
    L
    =
    60°
    ,
    M
    =
    120°
  • (iv)
    J
    =
    62°
    ,
    K
    =
    119°
    ,
    L
    =
    58°
    ,
    M
    =
    121°
  • (v)
    J
    =
    59°
    ,
    K
    =
    118°
    ,
    L
    =
    61°
    ,
    M
    =
    122°
Question 26
26.
    • In the adjoining figure,
    • FGHI
    • is a trapezium in which
    •  

      FG
       
       
      ∥
       

      HI
       
       
    • .
    • If
    •  
    • x = 115.5°
    • and
    •  
    • y = 143.86°
    • ,
    • find the measures of
    • ∠F
    • and
    • ∠G
    • .
  • (i)
    F
    =
    38.14°
    ,
    G
    =
    66.5°
  • (ii)
    F
    =
    35.14°
    ,
    G
    =
    63.5°
  • (iii)
    F
    =
    34.14°
    ,
    G
    =
    62.5°
  • (iv)
    F
    =
    36.14°
    ,
    G
    =
    64.5°
  • (v)
    F
    =
    37.14°
    ,
    G
    =
    65.5°
Question 27
27.
    • In the adjoining figure,
    • ABCD
    • is a kite in which
    • AB
    • =
    • DA
    • ,
    • BC
    • =
    • CD
    • and the diagonals
    •  

      BD
       
       
    • and
    •  

      AC
       
       
    • intersect at
    •  
    • O
    • .
    • If ∠OCD = 39.32° and ∠ABO = 65.76°, find the measure of each of the angles marked a,b,c,d and e.
  • (i)
    a = 50.68° , b = 25.24° , c = 64.76° , d = 52.68° , e = 39.32°
  • (ii)
    a = 50.68° , b = 25.24° , c = 64.76° , d = 52.68° , e = 37.32°
  • (iii)
    a = 50.68° , b = 25.24° , c = 64.76° , d = 50.68° , e = 39.32°
  • (iv)
    a = 50.68° , b = 25.24° , c = 65.76° , d = 50.68° , e = 39.32°
  • (v)
    a = 50.68° , b = 24.24° , c = 65.76° , d = 50.68° , e = 39.32°
Question 28
28.
    • In the adjoining figure,
    • ABCD
    • is a rhombus whose diagonals intersect at
    • O
    • .
    • If
    • ∠OAB
    • :
    • ∠ABO
    • =
    • 1 : 2
    • ,
    • find the angles of
    • △OAB
    • .
  • (i)
    O
    =
    92°
    ,
    A
    =
    30°
    ,
    B
    =
    58°
  • (ii)
    O
    =
    90°
    ,
    A
    =
    30°
    ,
    B
    =
    60°
  • (iii)
    O
    =
    88°
    ,
    A
    =
    32°
    ,
    B
    =
    60°
  • (iv)
    O
    =
    90°
    ,
    A
    =
    28°
    ,
    B
    =
    62°
  • (v)
    O
    =
    88°
    ,
    A
    =
    30°
    ,
    B
    =
    62°
Question 29
29.
    • The measures of three angles of a quadrilateral are
    • 59.49°
    • ,
    • 107.44°
    • and
    • 71.38°
    • . Find the fourth angle
  • (i)
    131.69°
  • (ii)
    126.69°
  • (iii)
    136.69°
  • (iv)
    121.69°
  • (v)
    151.69°
Question 30
30.
Find the missing angle in the given quadrilateral
  • (i)
    66.41°
  • (ii)
    91.41°
  • (iii)
    76.41°
  • (iv)
    71.41°
  • (v)
    61.41°
Question 31
31.
Find the missing angle in the given trapezium
  • (i)
    133.21°
  • (ii)
    123.21°
  • (iii)
    128.21°
  • (iv)
    148.21°
  • (v)
    118.21°
Question 32
32.
Find the missing angle in the given parallelogram
  • (i)
    88.88°
  • (ii)
    73.88°
  • (iii)
    78.88°
  • (iv)
    103.88°
  • (v)
    83.88°
Question 33
33.
Find the missing angle in the given rhombus
  • (i)
    106.26°
  • (ii)
    111.26°
  • (iii)
    136.26°
  • (iv)
    121.26°
  • (v)
    116.26°
Question 34
34.
    • In the adjoining figure,
    • CDEF
    • is a parallelogram and
    • GH
    • is such that
    •  

      GH
       
       
      ∥
       

      CE
       
       
    • If
    • ∠CFG = 23.49°
    • and
    • ∠EFH = 31.62°
    • ,
    • find the measure of
    • ∠EFC
    • .
  • (i)
    124.90°
  • (ii)
    125.90°
  • (iii)
    123.90°
  • (iv)
    122.90°
  • (v)
    126.90°
Question 35
35.
In the adjoining figure, ABCD is a square. A line segment DF cuts the side BC at F and the diagonal AC at E such that ∠DEC = 104.22° and ∠EFC = x°. Find the value of x .
  • (i)
    61.22°
  • (ii)
    59.22°
  • (iii)
    58.22°
  • (iv)
    60.22°
  • (v)
    57.22°
Question 36
36.
In the adjoining figure, MNOP is a rhombus and △QPO is an equilateral triangle. Q and M are on opposite sides of  OP. If ∠MNO = 63.95°, find the values of  x  and  y .
  • (i)
    x
    =
    26.02°
    ,
    y
    =
    28°
  • (ii)
    x
    =
    27.02°
    ,
    y
    =
    29°
  • (iii)
    x
    =
    29.02°
    ,
    y
    =
    31°
  • (iv)
    x
    =
    28.02°
    ,
    y
    =
    30°
  • (v)
    x
    =
    30.02°
    ,
    y
    =
    32°
Question 37
37.
In the adjoining figure, equilateral  △JIK surmounts square  GHIJ. If  IKG = x°, find the value of x.
  • (i)
    47°
  • (ii)
    43°
  • (iii)
    44°
  • (iv)
    45°
  • (v)
    46°
Question 38
38.
    • In the given figure,
    • GHIJ
    • is a rectangle whose diagonals intersect at
    • K
    • .
    • Diagonal
    • GI
    • is produced to
    • T
    • and
    • ∠HGT =
    • 137.49°
    • . Find the angles of
    • △KHI
    • .
  • (i)
    K
    =
    85.02°
    ,
    H
    =
    45.49°
    ,
    I
    =
    49.49°
  • (ii)
    K
    =
    87.02°
    ,
    H
    =
    47.49°
    ,
    I
    =
    45.49°
  • (iii)
    K
    =
    83.02°
    ,
    H
    =
    49.49°
    ,
    I
    =
    47.49°
  • (iv)
    K
    =
    83.02°
    ,
    H
    =
    47.49°
    ,
    I
    =
    49.49°
  • (v)
    K
    =
    85.02°
    ,
    H
    =
    47.49°
    ,
    I
    =
    47.49°
Question 39
39.
    • In the given figure,
    • PQRS
    • is a kite whose diagonals intersect at
    • T
    • .
    • If
    • ∠QRS = 79.61°
    • and
    • ∠RSP = 114.37°
    • , calculate
    • ∠TPQ
    • and
    • ∠RTQ
    • .
  • (i)
    x
    =
    24.82°
    ,
    y
    =
    89°
  • (ii)
    x
    =
    26.82°
    ,
    y
    =
    91°
  • (iii)
    x
    =
    25.82°
    ,
    y
    =
    90°
  • (iv)
    x
    =
    23.82°
    ,
    y
    =
    88°
  • (v)
    x
    =
    27.82°
    ,
    y
    =
    92°
Question 40
40.
    • △HFG
    • is an equilateral triangle in a square
    • DEFG
    • .
    • If
    • EG
    • and
    • HF
    • intersect at
    • I
    • ,
    • then find the value of x.
  • (i)
    75°
  • (ii)
    73°
  • (iii)
    74°
  • (iv)
    76°
  • (v)
    77°
Question 41
41.
    • In the adjoining figure,
    • I
    • is a point in the interior of
    • ∠KGL
    • .
    • If
    •  
    • IH
    • ⟂
    • GK
    • and
    • IJ
    • ⟂
    • GL
    • and
    • ∠KGL = 49°
    • ,
    • find the measure of x .
  • (i)
    230°
  • (ii)
    231°
  • (iii)
    228°
  • (iv)
    227°
  • (v)
    229°
Question 42
42.
    • In the given figure, HIJK is a parallelogram. V is the mid-point of JK.
    • IV
    • bisects
    • ∠I
    • . If x =
    • 53°
    • , find angle 'y'.
  • (i)
    39°
  • (ii)
    37°
  • (iii)
    38°
  • (iv)
    35°
  • (v)
    36°
Question 43
43.
In the given figure, DEFG is a rhombus. Given x = 54°, find the value of 'y'.
  • (i)
    35°
  • (ii)
    38°
  • (iii)
    37°
  • (iv)
    34°
  • (v)
    36°
Question 44
44.
    • In the given figure, IJKL is a parallelogram. JL is the diagonal
    • such that
    •  
    • IL = JL = JK
    • . Given
    • ∠I = 53°
    • , find
    • ∠LJK
  • (i)
    74°
  • (ii)
    72°
  • (iii)
    76°
  • (iv)
    75°
  • (v)
    73°
Question 45
45.
In the given figure, GHIJ is a parallelogram. GS and IT are perpendicular to the diagonal HJ. Given ∠SGH = 20°, find ∠IJH
  • (i)
    68°
  • (ii)
    71°
  • (iii)
    70°
  • (iv)
    69°
  • (v)
    72°
Question 46
46.
In the given figure, ABCD is a rhombus such that ∠B = 120°. Then △ABD is
  • (i)
    Right angled triangle
  • (ii)
    Equilateral triangle
  • (iii)
    Isosceles triangle
  • (iv)
    Obtuse angled triangle
Question 47
47.
In the given figure, HIJK is a parallelogram such that T is the mid-point of HI and  HI = 2KH. Find ∠KTJ
  • (i)
    89°
  • (ii)
    92°
  • (iii)
    88°
  • (iv)
    90°
  • (v)
    91°
    Assignment Key
  •  1) (iii)
  •  2) (iv)
  •  3) (iii)
  •  4) (iii)
  •  5) (iii)
  •  6) (ii)
  •  7) (iii)
  •  8) (i)
  •  9) (ii)
  •  10) (iii)
  •  11) (i)
  •  12) (iii)
  •  13) (v)
  •  14) (v)
  •  15) (i)
  •  16) (ii)
  •  17) (iv)
  •  18) (ii)
  •  19) (ii)
  •  20) (i)
  •  21) (iv)
  •  22) (i)
  •  23) (iii)
  •  24) (iv)
  •  25) (iii)
  •  26) (iv)
  •  27) (v)
  •  28) (ii)
  •  29) (iv)
  •  30) (v)
  •  31) (v)
  •  32) (ii)
  •  33) (i)
  •  34) (i)
  •  35) (ii)
  •  36) (iv)
  •  37) (iv)
  •  38) (v)
  •  39) (iii)
  •  40) (i)
  •  41) (v)
  •  42) (ii)
  •  43) (v)
  •  44) (i)
  •  45) (iii)
  •  46) (ii)
  •  47) (iv)