EduSahara™ Assignment
Name : Quadrilateral Angle Properties
Chapter : Quadrilaterals
Grade : ICSE Grade VII
License : Non Commercial Use
Question 1
1.
In parallelogram ABCD, if ∠C = 50.7°, then find the value of ∠A
  • (i)
    50.70°
  • (ii)
    52.70°
  • (iii)
    51.70°
  • (iv)
    48.70°
  • (v)
    49.70°
Question 2
2.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
  • (i)
    90°
  • (ii)
    88°
  • (iii)
    91°
  • (iv)
    92°
  • (v)
    89°
Question 3
3.
The sum of the interior angles of a quadrilateral is
  • (i)
    270°
  • (ii)
    90°
  • (iii)
    360°
  • (iv)
    180°
Question 4
4.
If ABCD is an isosceles trapezium, ∠D =
  • (i)
    ∠C
  • (ii)
    90°
  • (iii)
    ∠A
  • (iv)
    ∠B
Question 5
5.
DEFG is a rhombus in which ∠D = 120° .
 

EG
 
 
is the diagonal. Then △DEF is
  • (i)
    an obtuse angled triangle
  • (ii)
    an equilateral triangle
  • (iii)
    an isosceles triangle
  • (iv)
    a scalene triangle
  • (v)
    None of these
Question 6
6.
PQRS is a rhombus in which ∠P = 102° .
 

QS
 
 
is the diagonal. Then △PQR is
  • (i)
    a scalene triangle
  • (ii)
    None of these
  • (iii)
    an isosceles triangle
  • (iv)
    an obtuse angled triangle
  • (v)
    an equilateral triangle
Question 7
7.
The angles of a quadrilateral JKLM are in the ratio 5 : 13 : 17 : 37. Find the measure of each angle of the quadrilateral.
  • (i)
    J
    =
    25°
    ,
    K
    =
    65°
    ,
    L
    =
    85°
    ,
    M
    =
    185°
  • (ii)
    J
    =
    24°
    ,
    K
    =
    63°
    ,
    L
    =
    86°
    ,
    M
    =
    187°
  • (iii)
    J
    =
    27°
    ,
    K
    =
    64°
    ,
    L
    =
    83°
    ,
    M
    =
    186°
  • (iv)
    J
    =
    23°
    ,
    K
    =
    67°
    ,
    L
    =
    84°
    ,
    M
    =
    186°
  • (v)
    J
    =
    26°
    ,
    K
    =
    64°
    ,
    L
    =
    87°
    ,
    M
    =
    183°
Question 8
8.
Two adjacent angles of a parallelogram NOPQ are in the ratio 3 : 17. Find the measure of each of its angles.
  • (i)
    N
    =
    25°
    ,
    O
    =
    155°
    ,
    P
    =
    26°
    ,
    Q
    =
    154°
  • (ii)
    N
    =
    26°
    ,
    O
    =
    151°
    ,
    P
    =
    28°
    ,
    Q
    =
    155°
  • (iii)
    N
    =
    27°
    ,
    O
    =
    153°
    ,
    P
    =
    27°
    ,
    Q
    =
    153°
  • (iv)
    N
    =
    28°
    ,
    O
    =
    152°
    ,
    P
    =
    29°
    ,
    Q
    =
    151°
  • (v)
    N
    =
    29°
    ,
    O
    =
    152°
    ,
    P
    =
    25°
    ,
    Q
    =
    154°
Question 9
9.
    • In the adjoining figure,
    • GHIJ
    • is a parallelogram in which
    • ∠JGI = 40.8°
    • ,
    • ∠IGH = 30.51°
    • ,
    • ∠JKI = 104.34°
    • . Calculate
    • ∠GHJ
  • (i)
    44.15°
  • (ii)
    43.15°
  • (iii)
    46.15°
  • (iv)
    47.15°
  • (v)
    45.15°
Question 10
10.
    • In the adjoining figure,
    • IJKL
    • is a parallelogram in which
    • ∠LIK = 30.83°
    • ,
    • ∠KIJ = 22.92°
    • ,
    • ∠LMK = 107.81°
    • . Calculate
    • ∠KLJ
  • (i)
    49.27°
  • (ii)
    47.27°
  • (iii)
    48.27°
  • (iv)
    50.27°
  • (v)
    51.27°
Question 11
11.
    • In the adjoining figure,
    • LMNO
    • is a parallelogram in which
    • ∠OLN = 20.56°
    • ,
    • ∠NLM = 22.08°
    • ,
    • ∠OPN = 84.26°
    • . Calculate
    • ∠MNL
  • (i)
    22.56°
  • (ii)
    18.56°
  • (iii)
    20.56°
  • (iv)
    21.56°
  • (v)
    19.56°
Question 12
12.
    • In the adjoining figure,
    • IJKL
    • is a parallelogram in which
    • ∠LIK = 20.69°
    • ,
    • ∠KIJ = 35.18°
    • ,
    • ∠LMK = 57.77°
    • . Calculate
    • ∠LJK
  • (i)
    38.08°
  • (ii)
    39.08°
  • (iii)
    35.08°
  • (iv)
    37.08°
  • (v)
    36.08°
Question 13
13.
    • In the adjoining figure,
    • PQRS
    • is a rectangle.
    • If
    • ∠RPQ = 53.13°
    • , find
    • ∠STR
  • (i)
    73.74°
  • (ii)
    71.74°
  • (iii)
    74.74°
  • (iv)
    72.74°
  • (v)
    75.74°
Question 14
14.
Three angles of quadrilateral measure 89.24°, 131.05° and 88.96° respectively. Find the measure of the fourth angle
  • (i)
    49.75°
  • (ii)
    48.75°
  • (iii)
    51.75°
  • (iv)
    52.75°
  • (v)
    50.75°
Question 15
15.
Three angles of a quadrilateral are equal and the fourth angle measure 87.27°. What is the measure of each of the equal angles?
  • (i)
    92.91°
  • (ii)
    91.91°
  • (iii)
    88.91°
  • (iv)
    90.91°
  • (v)
    89.91°
Question 16
16.
Two angles of a quadrilateral are of measure 55.83° and 121.8° respectively and the other two angles are equal. Find the measure of each of the equal angles.
  • (i)
    92.19°
  • (ii)
    91.19°
  • (iii)
    89.19°
  • (iv)
    90.19°
  • (v)
    93.19°
Question 17
17.
A quadrilateral has three acute angles, each measuring 72°. What is the measure of its fourth angle?
  • (i)
    144.00°
  • (ii)
    145.00°
  • (iii)
    142.00°
  • (iv)
    146.00°
  • (v)
    143.00°
Question 18
18.
    • One angle of a parallelogram measures
    • A
    • =
    • 48.74°
    • .
    • Find the measure of each of its remaining angles.
  • (i)
    B
    =
    131.26°
    ,
    C
    =
    48.74°
    ,
    D
    =
    131.26°
  • (ii)
    B
    =
    129.26°
    ,
    C
    =
    46.74°
    ,
    D
    =
    129.26°
  • (iii)
    B
    =
    130.26°
    ,
    C
    =
    47.74°
    ,
    D
    =
    130.26°
  • (iv)
    B
    =
    132.26°
    ,
    C
    =
    49.74°
    ,
    D
    =
    132.26°
  • (v)
    B
    =
    133.26°
    ,
    C
    =
    50.74°
    ,
    D
    =
    133.26°
Question 19
19.
    • Two adjacent angles of a parallelogram are in the ratio
    • 14 : 76
    • .
    • Find the measure of each of its angles.
  • (i)
    A
    =
    30°
    ,
    B
    =
    151°
    ,
    C
    =
    26°
    ,
    D
    =
    153°
  • (ii)
    A
    =
    28°
    ,
    B
    =
    152°
    ,
    C
    =
    28°
    ,
    D
    =
    152°
  • (iii)
    A
    =
    29°
    ,
    B
    =
    151°
    ,
    C
    =
    30°
    ,
    D
    =
    150°
  • (iv)
    A
    =
    27°
    ,
    B
    =
    150°
    ,
    C
    =
    29°
    ,
    D
    =
    154°
  • (v)
    A
    =
    26°
    ,
    B
    =
    154°
    ,
    C
    =
    27°
    ,
    D
    =
    153°
Question 20
20.
    • In the figure given below,
    • DEFG
    • is a rectangle.
    • Find the values of x and y
  • (i)
    x
    =
    28.05°
    ,
    y
    =
    57.1°
  • (ii)
    x
    =
    31.05°
    ,
    y
    =
    60.1°
  • (iii)
    x
    =
    30.05°
    ,
    y
    =
    59.1°
  • (iv)
    x
    =
    29.05°
    ,
    y
    =
    58.1°
  • (v)
    x
    =
    27.05°
    ,
    y
    =
    56.1°
Question 21
21.
    • In the figure given below,
    • MNOP
    • is a rectangle.
    • Find the values of x and y
  • (i)
    x
    =
    38.81°
    ,
    y
    =
    49.19°
  • (ii)
    x
    =
    40.81°
    ,
    y
    =
    51.19°
  • (iii)
    x
    =
    41.81°
    ,
    y
    =
    52.19°
  • (iv)
    x
    =
    37.81°
    ,
    y
    =
    48.19°
  • (v)
    x
    =
    39.81°
    ,
    y
    =
    50.19°
Question 22
22.
    • In the figure given below,
    • CDEF
    • is a rhombus.
    • Find the values of x and y
  • (i)
    x
    =
    43°
    ,
    y
    =
    43°
  • (ii)
    x
    =
    46°
    ,
    y
    =
    46°
  • (iii)
    x
    =
    45°
    ,
    y
    =
    45°
  • (iv)
    x
    =
    47°
    ,
    y
    =
    47°
  • (v)
    x
    =
    44°
    ,
    y
    =
    44°
Question 23
23.
    • In the figure given below,
    • OPQR
    • is a rhombus.
    • Find the values of x and y
  • (i)
    x
    =
    58.95°
    ,
    y
    =
    58.95°
  • (ii)
    x
    =
    59.95°
    ,
    y
    =
    59.95°
  • (iii)
    x
    =
    55.95°
    ,
    y
    =
    55.95°
  • (iv)
    x
    =
    56.95°
    ,
    y
    =
    56.95°
  • (v)
    x
    =
    57.95°
    ,
    y
    =
    57.95°
Question 24
24.
    • In the figure given below,
    • ABCD
    • is a rhombus.
    • Find the values of x and y
  • (i)
    x
    =
    38.48°
    ,
    y
    =
    47.52°
  • (ii)
    x
    =
    41.48°
    ,
    y
    =
    50.52°
  • (iii)
    x
    =
    40.48°
    ,
    y
    =
    49.52°
  • (iv)
    x
    =
    42.48°
    ,
    y
    =
    51.52°
  • (v)
    x
    =
    39.48°
    ,
    y
    =
    48.52°
Question 25
25.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
  • (i)
    H
    =
    59°
    ,
    I
    =
    118°
    ,
    J
    =
    61°
    ,
    K
    =
    122°
  • (ii)
    H
    =
    62°
    ,
    I
    =
    119°
    ,
    J
    =
    58°
    ,
    K
    =
    121°
  • (iii)
    H
    =
    60°
    ,
    I
    =
    120°
    ,
    J
    =
    60°
    ,
    K
    =
    120°
  • (iv)
    H
    =
    61°
    ,
    I
    =
    119°
    ,
    J
    =
    62°
    ,
    K
    =
    118°
  • (v)
    H
    =
    58°
    ,
    I
    =
    122°
    ,
    J
    =
    59°
    ,
    K
    =
    121°
Question 26
26.
    • In the adjoining figure,
    • HIJK
    • is a trapezium in which
    •  

      HI
       
       
      ∥
       

      JK
       
       
    • .
    • If
    •  
    • x = 47.59°
    • and
    •  
    • y = 72.2°
    • ,
    • find the measures of
    • ∠J
    • and
    • ∠K
    • .
  • (i)
    J
    =
    107.8°
    ,
    K
    =
    132.41°
  • (ii)
    J
    =
    109.8°
    ,
    K
    =
    134.41°
  • (iii)
    J
    =
    106.8°
    ,
    K
    =
    131.41°
  • (iv)
    J
    =
    105.8°
    ,
    K
    =
    130.41°
  • (v)
    J
    =
    108.8°
    ,
    K
    =
    133.41°
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 = 38.66° and ∠ABO = 55.59°, find the measure of each of the angles marked a,b,c,d and e.
  • (i)
    a = 51.34° , b = 35.41° , c = 55.59° , d = 51.34° , e = 38.66°
  • (ii)
    a = 51.34° , b = 34.41° , c = 55.59° , d = 51.34° , e = 38.66°
  • (iii)
    a = 51.34° , b = 35.41° , c = 54.59° , d = 53.34° , e = 38.66°
  • (iv)
    a = 51.34° , b = 35.41° , c = 54.59° , d = 53.34° , e = 36.66°
  • (v)
    a = 51.34° , b = 35.41° , c = 54.59° , d = 51.34° , e = 38.66°
Question 28
28.
    • In the adjoining figure,
    • ABCD
    • is a rhombus whose diagonals intersect at
    • O
    • .
    • If
    • ∠OAB
    • :
    • ∠ABO
    • =
    • 4 : 6
    • ,
    • find the angles of
    • △OAB
    • .
  • (i)
    O
    =
    92°
    ,
    A
    =
    36°
    ,
    B
    =
    52°
  • (ii)
    O
    =
    90°
    ,
    A
    =
    36°
    ,
    B
    =
    54°
  • (iii)
    O
    =
    90°
    ,
    A
    =
    34°
    ,
    B
    =
    56°
  • (iv)
    O
    =
    88°
    ,
    A
    =
    38°
    ,
    B
    =
    54°
  • (v)
    O
    =
    88°
    ,
    A
    =
    36°
    ,
    B
    =
    56°
Question 29
29.
    • The measures of three angles of a quadrilateral are
    • 79.04°
    • ,
    • 115.26°
    • and
    • 57.61°
    • . Find the fourth angle
  • (i)
    138.09°
  • (ii)
    108.09°
  • (iii)
    113.09°
  • (iv)
    118.09°
  • (v)
    123.09°
Question 30
30.
Find the missing angle in the given quadrilateral
  • (i)
    93.22°
  • (ii)
    63.22°
  • (iii)
    73.22°
  • (iv)
    78.22°
  • (v)
    68.22°
Question 31
31.
Find the missing angle in the given trapezium
  • (i)
    131.9°
  • (ii)
    126.9°
  • (iii)
    121.9°
  • (iv)
    136.9°
  • (v)
    151.9°
Question 32
32.
Find the missing angle in the given parallelogram
  • (i)
    107.47°
  • (ii)
    112.47°
  • (iii)
    137.47°
  • (iv)
    117.47°
  • (v)
    122.47°
Question 33
33.
Find the missing angle in the given rhombus
  • (i)
    76.88°
  • (ii)
    81.88°
  • (iii)
    71.88°
  • (iv)
    101.88°
  • (v)
    86.88°
Question 34
34.
    • In the adjoining figure,
    • OPQR
    • is a parallelogram and
    • ST
    • is such that
    •  

      ST
       
       
      ∥
       

      OQ
       
       
    • If
    • ∠ORS = 36.29°
    • and
    • ∠QRT = 41.12°
    • ,
    • find the measure of
    • ∠OPQ
    • .
  • (i)
    104.59°
  • (ii)
    103.59°
  • (iii)
    101.59°
  • (iv)
    100.59°
  • (v)
    102.59°
Question 35
35.
In the adjoining figure, BCDE is a square. A line segment EG cuts the side CD at G and the diagonal BD at F such that ∠EFD = 102.36° and ∠FGD = x°. Find the value of x .
  • (i)
    59.36°
  • (ii)
    55.36°
  • (iii)
    57.36°
  • (iv)
    58.36°
  • (v)
    56.36°
Question 36
36.
In the adjoining figure, LMNO is a rhombus and △PON is an equilateral triangle. P and M are on opposite sides of  NO. If ∠OLM = 90°, find the values of  x  and  y .
  • (i)
    x
    =
    28°
    ,
    y
    =
    13°
  • (ii)
    x
    =
    32°
    ,
    y
    =
    17°
  • (iii)
    x
    =
    31°
    ,
    y
    =
    16°
  • (iv)
    x
    =
    30°
    ,
    y
    =
    15°
  • (v)
    x
    =
    29°
    ,
    y
    =
    14°
Question 37
37.
In the adjoining figure, equilateral  △LKM surmounts square  IJKL. If  KMI = x°, find the value of x.
  • (i)
    45°
  • (ii)
    44°
  • (iii)
    46°
  • (iv)
    43°
  • (v)
    47°
Question 38
38.
    • In the given figure,
    • EFGH
    • is a rectangle whose diagonals intersect at
    • I
    • .
    • Diagonal
    • EG
    • is produced to
    • T
    • and
    • ∠FET =
    • 119.74°
    • . Find the angles of
    • △IFG
    • .
  • (i)
    I
    =
    118.52°
    ,
    F
    =
    31.74°
    ,
    G
    =
    29.74°
  • (ii)
    I
    =
    120.52°
    ,
    F
    =
    27.74°
    ,
    G
    =
    31.74°
  • (iii)
    I
    =
    122.52°
    ,
    F
    =
    29.74°
    ,
    G
    =
    27.74°
  • (iv)
    I
    =
    120.52°
    ,
    F
    =
    29.74°
    ,
    G
    =
    29.74°
  • (v)
    I
    =
    118.52°
    ,
    F
    =
    29.74°
    ,
    G
    =
    31.74°
Question 39
39.
    • In the given figure,
    • JKLM
    • is a kite whose diagonals intersect at
    • N
    • .
    • If
    • ∠MJK = 74.53°
    • and
    • ∠KLM = 43.16°
    • , calculate
    • ∠NMJ
    • and
    • ∠NKL
    • .
  • (i)
    x
    =
    52.73°
    ,
    y
    =
    68.42°
  • (ii)
    x
    =
    51.73°
    ,
    y
    =
    67.42°
  • (iii)
    x
    =
    50.73°
    ,
    y
    =
    66.42°
  • (iv)
    x
    =
    53.73°
    ,
    y
    =
    69.42°
  • (v)
    x
    =
    54.73°
    ,
    y
    =
    70.42°
Question 40
40.
    • △ONK
    • is an equilateral triangle in a square
    • KLMN
    • .
    • If
    • LN
    • and
    • KO
    • intersect at
    • P
    • ,
    • then find the value of x.
  • (i)
    76°
  • (ii)
    74°
  • (iii)
    73°
  • (iv)
    75°
  • (v)
    77°
Question 41
41.
    • In the adjoining figure,
    • M
    • is a point in the interior of
    • ∠OKP
    • .
    • If
    •  
    • ML
    • ⟂
    • KO
    • and
    • MN
    • ⟂
    • KP
    • and
    • ∠OKP = 36°
    • ,
    • find the measure of x .
  • (i)
    215°
  • (ii)
    214°
  • (iii)
    218°
  • (iv)
    217°
  • (v)
    216°
Question 42
42.
    • In the given figure, EFGH is a parallelogram. U is the mid-point of GH.
    • FU
    • bisects
    • ∠F
    • . If x =
    • 52°
    • , find angle 'y'.
  • (i)
    38°
  • (ii)
    40°
  • (iii)
    37°
  • (iv)
    39°
  • (v)
    36°
Question 43
43.
In the given figure, FGHI is a rhombus. Given x = 58°, find the value of 'y'.
  • (i)
    34°
  • (ii)
    33°
  • (iii)
    31°
  • (iv)
    30°
  • (v)
    32°
Question 44
44.
    • In the given figure, IJKL is a parallelogram. JL is the diagonal
    • such that
    •  
    • IL = JL = JK
    • . Given
    • ∠I = 47°
    • , find
    • ∠LJK
  • (i)
    85°
  • (ii)
    87°
  • (iii)
    84°
  • (iv)
    88°
  • (v)
    86°
Question 45
45.
In the given figure, ABCD is a parallelogram. AP and CQ are perpendicular to the diagonal BD. Given ∠QCD = 11°, find ∠DBA
  • (i)
    80°
  • (ii)
    81°
  • (iii)
    79°
  • (iv)
    78°
  • (v)
    77°
Question 46
46.
In the given figure, IJKL is a rhombus such that ∠J = 120°. Then △IJL is
  • (i)
    Obtuse angled triangle
  • (ii)
    Isosceles triangle
  • (iii)
    Right angled triangle
  • (iv)
    Equilateral triangle
Question 47
47.
In the given figure, EFGH is a parallelogram such that P is the mid-point of EF and  EF = 2HE. Find ∠HPG
  • (i)
    91°
  • (ii)
    88°
  • (iii)
    89°
  • (iv)
    90°
  • (v)
    92°
    Assignment Key
  •  1) (i)
  •  2) (i)
  •  3) (iii)
  •  4) (i)
  •  5) (ii)
  •  6) (iii)
  •  7) (i)
  •  8) (iii)
  •  9) (v)
  •  10) (i)
  •  11) (iii)
  •  12) (iv)
  •  13) (i)
  •  14) (v)
  •  15) (iv)
  •  16) (ii)
  •  17) (i)
  •  18) (i)
  •  19) (ii)
  •  20) (iv)
  •  21) (v)
  •  22) (iii)
  •  23) (v)
  •  24) (iii)
  •  25) (iii)
  •  26) (i)
  •  27) (ii)
  •  28) (ii)
  •  29) (ii)
  •  30) (ii)
  •  31) (iii)
  •  32) (i)
  •  33) (iii)
  •  34) (v)
  •  35) (iii)
  •  36) (iv)
  •  37) (i)
  •  38) (iv)
  •  39) (i)
  •  40) (iv)
  •  41) (v)
  •  42) (i)
  •  43) (v)
  •  44) (v)
  •  45) (iii)
  •  46) (iv)
  •  47) (iv)