EduSahara™ Assignment
Name : Quadrilateral Angle Properties
Chapter : Quadrilaterals
Grade : ICSE Grade VII
License : Non Commercial Use
Question 1
1.
In parallelogram ABCD, if ∠A = 97.37°, then find the value of ∠C
  • (i)
    95.37°
  • (ii)
    98.37°
  • (iii)
    97.37°
  • (iv)
    99.37°
  • (v)
    96.37°
Question 2
2.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
  • (i)
    92°
  • (ii)
    88°
  • (iii)
    89°
  • (iv)
    90°
  • (v)
    91°
Question 3
3.
The sum of the interior angles of a quadrilateral is
  • (i)
    360°
  • (ii)
    90°
  • (iii)
    180°
  • (iv)
    270°
Question 4
4.
If ABCD is an isosceles trapezium, ∠A =
  • (i)
    ∠D
  • (ii)
    ∠C
  • (iii)
    90°
  • (iv)
    ∠B
Question 5
5.
LMNO is a rhombus in which ∠L = 120° .
 

MO
 
 
is the diagonal. Then △LMN is
  • (i)
    an equilateral triangle
  • (ii)
    an obtuse angled triangle
  • (iii)
    an isosceles triangle
  • (iv)
    None of these
  • (v)
    a scalene triangle
Question 6
6.
CDEF is a rhombus in which ∠C = 112° .
 

DF
 
 
is the diagonal. Then △CDE is
  • (i)
    an isosceles triangle
  • (ii)
    None of these
  • (iii)
    an obtuse angled triangle
  • (iv)
    a scalene triangle
  • (v)
    an equilateral triangle
Question 7
7.
The angles of a quadrilateral EFGH are in the ratio 4 : 3 : 5 : 8. Find the measure of each angle of the quadrilateral.
  • (i)
    E
    =
    74°
    ,
    F
    =
    53°
    ,
    G
    =
    88°
    ,
    H
    =
    145°
  • (ii)
    E
    =
    73°
    ,
    F
    =
    53°
    ,
    G
    =
    92°
    ,
    H
    =
    142°
  • (iii)
    E
    =
    72°
    ,
    F
    =
    54°
    ,
    G
    =
    90°
    ,
    H
    =
    144°
  • (iv)
    E
    =
    71°
    ,
    F
    =
    52°
    ,
    G
    =
    91°
    ,
    H
    =
    146°
  • (v)
    E
    =
    70°
    ,
    F
    =
    56°
    ,
    G
    =
    89°
    ,
    H
    =
    145°
Question 8
8.
Two adjacent angles of a parallelogram BCDE are in the ratio 10 : 20. Find the measure of each of its angles.
  • (i)
    B
    =
    58°
    ,
    C
    =
    122°
    ,
    D
    =
    59°
    ,
    E
    =
    121°
  • (ii)
    B
    =
    60°
    ,
    C
    =
    120°
    ,
    D
    =
    60°
    ,
    E
    =
    120°
  • (iii)
    B
    =
    62°
    ,
    C
    =
    119°
    ,
    D
    =
    58°
    ,
    E
    =
    121°
  • (iv)
    B
    =
    61°
    ,
    C
    =
    119°
    ,
    D
    =
    62°
    ,
    E
    =
    118°
  • (v)
    B
    =
    59°
    ,
    C
    =
    118°
    ,
    D
    =
    61°
    ,
    E
    =
    122°
Question 9
9.
    • In the adjoining figure,
    • NOPQ
    • is a parallelogram in which
    • ∠QNP = 33.28°
    • ,
    • ∠PNO = 17.43°
    • ,
    • ∠QRP = 128.35°
    • . Calculate
    • ∠NOQ
  • (i)
    33.22°
  • (ii)
    34.22°
  • (iii)
    35.22°
  • (iv)
    36.22°
  • (v)
    32.22°
Question 10
10.
    • In the adjoining figure,
    • BCDE
    • is a parallelogram in which
    • ∠EBD = 22.57°
    • ,
    • ∠DBC = 38.87°
    • ,
    • ∠EFD = 59.77°
    • . Calculate
    • ∠DEC
  • (i)
    81.36°
  • (ii)
    80.36°
  • (iii)
    83.36°
  • (iv)
    82.36°
  • (v)
    79.36°
Question 11
11.
    • In the adjoining figure,
    • NOPQ
    • is a parallelogram in which
    • ∠QNP = 17.95°
    • ,
    • ∠PNO = 15.37°
    • ,
    • ∠QRP = 105.49°
    • . Calculate
    • ∠OPN
  • (i)
    15.95°
  • (ii)
    17.95°
  • (iii)
    19.95°
  • (iv)
    18.95°
  • (v)
    16.95°
Question 12
12.
    • In the adjoining figure,
    • KLMN
    • is a parallelogram in which
    • ∠NKM = 45.92°
    • ,
    • ∠MKL = 29.41°
    • ,
    • ∠NOM = 110.83°
    • . Calculate
    • ∠NLM
  • (i)
    62.90°
  • (ii)
    64.90°
  • (iii)
    66.90°
  • (iv)
    65.90°
  • (v)
    63.90°
Question 13
13.
    • In the adjoining figure,
    • DEFG
    • is a rectangle.
    • If
    • ∠FDE = 43.45°
    • , find
    • ∠GHF
  • (i)
    94.10°
  • (ii)
    93.10°
  • (iii)
    95.10°
  • (iv)
    92.10°
  • (v)
    91.10°
Question 14
14.
Three angles of quadrilateral measure 81.79°, 60° and 98.21° respectively. Find the measure of the fourth angle
  • (i)
    120.00°
  • (ii)
    122.00°
  • (iii)
    119.00°
  • (iv)
    118.00°
  • (v)
    121.00°
Question 15
15.
Three angles of a quadrilateral are equal and the fourth angle measure 77.97°. What is the measure of each of the equal angles?
  • (i)
    94.01°
  • (ii)
    95.01°
  • (iii)
    92.01°
  • (iv)
    93.01°
  • (v)
    96.01°
Question 16
16.
Two angles of a quadrilateral are of measure 44.47° and 128.19° respectively and the other two angles are equal. Find the measure of each of the equal angles.
  • (i)
    91.67°
  • (ii)
    92.67°
  • (iii)
    94.67°
  • (iv)
    93.67°
  • (v)
    95.67°
Question 17
17.
A quadrilateral has three acute angles, each measuring 38°. What is the measure of its fourth angle?
  • (i)
    246.00°
  • (ii)
    247.00°
  • (iii)
    244.00°
  • (iv)
    245.00°
  • (v)
    248.00°
Question 18
18.
    • One angle of a parallelogram measures
    • J
    • =
    • 41.8°
    • .
    • Find the measure of each of its remaining angles.
  • (i)
    K
    =
    140.2°
    ,
    L
    =
    43.8°
    ,
    M
    =
    140.2°
  • (ii)
    K
    =
    136.2°
    ,
    L
    =
    39.8°
    ,
    M
    =
    136.2°
  • (iii)
    K
    =
    138.2°
    ,
    L
    =
    41.8°
    ,
    M
    =
    138.2°
  • (iv)
    K
    =
    139.2°
    ,
    L
    =
    42.8°
    ,
    M
    =
    139.2°
  • (v)
    K
    =
    137.2°
    ,
    L
    =
    40.8°
    ,
    M
    =
    137.2°
Question 19
19.
    • Two adjacent angles of a parallelogram are in the ratio
    • 3 : 7
    • .
    • Find the measure of each of its angles.
  • (i)
    A
    =
    53°
    ,
    B
    =
    124°
    ,
    C
    =
    55°
    ,
    D
    =
    128°
  • (ii)
    A
    =
    55°
    ,
    B
    =
    125°
    ,
    C
    =
    56°
    ,
    D
    =
    124°
  • (iii)
    A
    =
    54°
    ,
    B
    =
    126°
    ,
    C
    =
    54°
    ,
    D
    =
    126°
  • (iv)
    A
    =
    56°
    ,
    B
    =
    125°
    ,
    C
    =
    52°
    ,
    D
    =
    127°
  • (v)
    A
    =
    52°
    ,
    B
    =
    128°
    ,
    C
    =
    53°
    ,
    D
    =
    127°
Question 20
20.
    • In the figure given below,
    • JKLM
    • is a rectangle.
    • Find the values of x and y
  • (i)
    x
    =
    32.02°
    ,
    y
    =
    65.04°
  • (ii)
    x
    =
    33.02°
    ,
    y
    =
    66.04°
  • (iii)
    x
    =
    35.02°
    ,
    y
    =
    68.04°
  • (iv)
    x
    =
    31.02°
    ,
    y
    =
    64.04°
  • (v)
    x
    =
    34.02°
    ,
    y
    =
    67.04°
Question 21
21.
    • In the figure given below,
    • PQRS
    • is a rectangle.
    • Find the values of x and y
  • (i)
    x
    =
    39.18°
    ,
    y
    =
    46.82°
  • (ii)
    x
    =
    43.18°
    ,
    y
    =
    50.82°
  • (iii)
    x
    =
    40.18°
    ,
    y
    =
    47.82°
  • (iv)
    x
    =
    42.18°
    ,
    y
    =
    49.82°
  • (v)
    x
    =
    41.18°
    ,
    y
    =
    48.82°
Question 22
22.
    • In the figure given below,
    • CDEF
    • is a rhombus.
    • Find the values of x and y
  • (i)
    x
    =
    32.2°
    ,
    y
    =
    32.2°
  • (ii)
    x
    =
    33.2°
    ,
    y
    =
    33.2°
  • (iii)
    x
    =
    34.2°
    ,
    y
    =
    34.2°
  • (iv)
    x
    =
    35.2°
    ,
    y
    =
    35.2°
  • (v)
    x
    =
    36.2°
    ,
    y
    =
    36.2°
Question 23
23.
    • In the figure given below,
    • ABCD
    • is a rhombus.
    • Find the values of x and y
  • (i)
    x
    =
    33.33°
    ,
    y
    =
    33.33°
  • (ii)
    x
    =
    36.33°
    ,
    y
    =
    36.33°
  • (iii)
    x
    =
    37.33°
    ,
    y
    =
    37.33°
  • (iv)
    x
    =
    35.33°
    ,
    y
    =
    35.33°
  • (v)
    x
    =
    34.33°
    ,
    y
    =
    34.33°
Question 24
24.
    • In the figure given below,
    • BCDE
    • is a rhombus.
    • Find the values of x and y
  • (i)
    x
    =
    17.59°
    ,
    y
    =
    68.41°
  • (ii)
    x
    =
    21.59°
    ,
    y
    =
    72.41°
  • (iii)
    x
    =
    18.59°
    ,
    y
    =
    69.41°
  • (iv)
    x
    =
    20.59°
    ,
    y
    =
    71.41°
  • (v)
    x
    =
    19.59°
    ,
    y
    =
    70.41°
Question 25
25.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
  • (i)
    G
    =
    62°
    ,
    H
    =
    119°
    ,
    I
    =
    58°
    ,
    J
    =
    121°
  • (ii)
    G
    =
    58°
    ,
    H
    =
    122°
    ,
    I
    =
    59°
    ,
    J
    =
    121°
  • (iii)
    G
    =
    61°
    ,
    H
    =
    119°
    ,
    I
    =
    62°
    ,
    J
    =
    118°
  • (iv)
    G
    =
    60°
    ,
    H
    =
    120°
    ,
    I
    =
    60°
    ,
    J
    =
    120°
  • (v)
    G
    =
    59°
    ,
    H
    =
    118°
    ,
    I
    =
    61°
    ,
    J
    =
    122°
Question 26
26.
    • In the adjoining figure,
    • CDEF
    • is a trapezium in which
    •  

      CD
       
       
      ∥
       

      EF
       
       
    • .
    • If
    •  
    • x = 98.57°
    • and
    •  
    • y = 133.39°
    • ,
    • find the measures of
    • ∠C
    • and
    • ∠D
    • .
  • (i)
    C
    =
    44.61°
    ,
    D
    =
    79.43°
  • (ii)
    C
    =
    45.61°
    ,
    D
    =
    80.43°
  • (iii)
    C
    =
    47.61°
    ,
    D
    =
    82.43°
  • (iv)
    C
    =
    48.61°
    ,
    D
    =
    83.43°
  • (v)
    C
    =
    46.61°
    ,
    D
    =
    81.43°
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 = 19.41° and ∠ABO = 60.95°, find the measure of each of the angles marked a,b,c,d and e.
  • (i)
    a = 70.59° , b = 30.05° , c = 59.95° , d = 72.59° , e = 19.41°
  • (ii)
    a = 70.59° , b = 30.05° , c = 59.95° , d = 72.59° , e = 17.41°
  • (iii)
    a = 70.59° , b = 30.05° , c = 60.95° , d = 70.59° , e = 19.41°
  • (iv)
    a = 70.59° , b = 29.05° , c = 60.95° , d = 70.59° , e = 19.41°
  • (v)
    a = 70.59° , b = 30.05° , c = 59.95° , d = 70.59° , e = 19.41°
Question 28
28.
    • In the adjoining figure,
    • ABCD
    • is a rhombus whose diagonals intersect at
    • O
    • .
    • If
    • ∠OAB
    • :
    • ∠ABO
    • =
    • 2 : 3
    • ,
    • find the angles of
    • △OAB
    • .
  • (i)
    O
    =
    88°
    ,
    A
    =
    36°
    ,
    B
    =
    56°
  • (ii)
    O
    =
    92°
    ,
    A
    =
    36°
    ,
    B
    =
    52°
  • (iii)
    O
    =
    90°
    ,
    A
    =
    34°
    ,
    B
    =
    56°
  • (iv)
    O
    =
    88°
    ,
    A
    =
    38°
    ,
    B
    =
    54°
  • (v)
    O
    =
    90°
    ,
    A
    =
    36°
    ,
    B
    =
    54°
Question 29
29.
    • The measures of three angles of a quadrilateral are
    • 62.33°
    • ,
    • 117.67°
    • and
    • 62.33°
    • . Find the fourth angle
  • (i)
    117.67°
  • (ii)
    132.67°
  • (iii)
    127.67°
  • (iv)
    122.67°
  • (v)
    147.67°
Question 30
30.
Find the missing angle in the given quadrilateral
  • (i)
    116.11°
  • (ii)
    121.11°
  • (iii)
    131.11°
  • (iv)
    126.11°
  • (v)
    146.11°
Question 31
31.
Find the missing angle in the given trapezium
  • (i)
    130.65°
  • (ii)
    115.65°
  • (iii)
    110.65°
  • (iv)
    100.65°
  • (v)
    105.65°
Question 32
32.
Find the missing angle in the given parallelogram
  • (i)
    69.86°
  • (ii)
    59.86°
  • (iii)
    89.86°
  • (iv)
    64.86°
  • (v)
    74.86°
Question 33
33.
Find the missing angle in the given rhombus
  • (i)
    108.12°
  • (ii)
    138.12°
  • (iii)
    123.12°
  • (iv)
    118.12°
  • (v)
    113.12°
Question 34
34.
    • In the adjoining figure,
    • FGHI
    • is a parallelogram and
    • JK
    • is such that
    •  

      JK
       
       
      ∥
       

      FH
       
       
    • If
    • ∠FIJ = 23.05°
    • and
    • ∠HIK = 24.08°
    • ,
    • find the measure of
    • ∠FGH
    • .
  • (i)
    132.88°
  • (ii)
    130.88°
  • (iii)
    131.88°
  • (iv)
    133.88°
  • (v)
    134.88°
Question 35
35.
In the adjoining figure, DEFG is a square. A line segment GI cuts the side EF at I and the diagonal DF at H such that ∠GHF = 108.43° and ∠HIF = x°. Find the value of x .
  • (i)
    62.43°
  • (ii)
    63.43°
  • (iii)
    65.43°
  • (iv)
    64.43°
  • (v)
    61.43°
Question 36
36.
In the adjoining figure, PQRS is a rhombus and △TSR is an equilateral triangle. T and P are on opposite sides of  RS. If ∠PQR = 86.36°, find the values of  x  and  y .
  • (i)
    x
    =
    15.82°
    ,
    y
    =
    29°
  • (ii)
    x
    =
    14.82°
    ,
    y
    =
    28°
  • (iii)
    x
    =
    16.82°
    ,
    y
    =
    30°
  • (iv)
    x
    =
    18.82°
    ,
    y
    =
    32°
  • (v)
    x
    =
    17.82°
    ,
    y
    =
    31°
Question 37
37.
In the adjoining figure, equilateral  △SRT surmounts square  PQRS. If  RTQ = x°, find the value of x.
  • (i)
    16°
  • (ii)
    13°
  • (iii)
    15°
  • (iv)
    14°
  • (v)
    17°
Question 38
38.
    • In the given figure,
    • KLMN
    • is a rectangle whose diagonals intersect at
    • O
    • .
    • Diagonal
    • KM
    • is produced to
    • T
    • and
    • ∠NMT =
    • 125.84°
    • . Find the angles of
    • △OLM
    • .
  • (i)
    O
    =
    108.32°
    ,
    L
    =
    35.84°
    ,
    M
    =
    35.84°
  • (ii)
    O
    =
    108.32°
    ,
    L
    =
    33.84°
    ,
    M
    =
    37.84°
  • (iii)
    O
    =
    110.32°
    ,
    L
    =
    35.84°
    ,
    M
    =
    33.84°
  • (iv)
    O
    =
    106.32°
    ,
    L
    =
    35.84°
    ,
    M
    =
    37.84°
  • (v)
    O
    =
    106.32°
    ,
    L
    =
    37.84°
    ,
    M
    =
    35.84°
Question 39
39.
    • In the given figure,
    • MNOP
    • is a kite whose diagonals intersect at
    • Q
    • .
    • If
    • ∠PMN = 61.53°
    • and
    • ∠NOP = 77.17°
    • , calculate
    • ∠QPM
    • and
    • ∠QNO
    • .
  • (i)
    x
    =
    61.23°
    ,
    y
    =
    53.41°
  • (ii)
    x
    =
    58.23°
    ,
    y
    =
    50.41°
  • (iii)
    x
    =
    59.23°
    ,
    y
    =
    51.41°
  • (iv)
    x
    =
    60.23°
    ,
    y
    =
    52.41°
  • (v)
    x
    =
    57.23°
    ,
    y
    =
    49.41°
Question 40
40.
    • △PLM
    • is an equilateral triangle in a square
    • LMNO
    • .
    • If
    • MO
    • and
    • PL
    • intersect at
    • Q
    • ,
    • then find the value of x.
  • (i)
    76°
  • (ii)
    74°
  • (iii)
    77°
  • (iv)
    75°
  • (v)
    73°
Question 41
41.
    • In the adjoining figure,
    • I
    • is a point in the interior of
    • ∠KGL
    • .
    • If
    •  
    • IH
    • ⟂
    • GK
    • and
    • IJ
    • ⟂
    • GL
    • and
    • ∠KGL = 51°
    • ,
    • find the measure of x .
  • (i)
    233°
  • (ii)
    231°
  • (iii)
    229°
  • (iv)
    232°
  • (v)
    230°
Question 42
42.
    • In the given figure, EFGH is a parallelogram. R is the mid-point of GH.
    • FR
    • bisects
    • ∠F
    • . If x =
    • 52°
    • , find angle 'y'.
  • (i)
    38°
  • (ii)
    37°
  • (iii)
    39°
  • (iv)
    36°
  • (v)
    40°
Question 43
43.
In the given figure, ABCD is a rhombus. Given x = 58°, find the value of 'y'.
  • (i)
    30°
  • (ii)
    34°
  • (iii)
    31°
  • (iv)
    32°
  • (v)
    33°
Question 44
44.
    • In the given figure, HIJK is a parallelogram. IK is the diagonal
    • such that
    •  
    • HK = IK = IJ
    • . Given
    • ∠H = 60°
    • , find
    • ∠KIJ
  • (i)
    61°
  • (ii)
    59°
  • (iii)
    62°
  • (iv)
    60°
  • (v)
    58°
Question 45
45.
In the given figure, GHIJ is a parallelogram. GN and IO are perpendicular to the diagonal HJ. Given ∠OIJ = 23°, find ∠JHG
  • (i)
    65°
  • (ii)
    66°
  • (iii)
    68°
  • (iv)
    69°
  • (v)
    67°
Question 46
46.
In the given figure, IJKL is a rhombus such that ∠J = 120°. Then △IJL is
  • (i)
    Right angled triangle
  • (ii)
    Isosceles triangle
  • (iii)
    Obtuse angled triangle
  • (iv)
    Equilateral triangle
Question 47
47.
In the given figure, EFGH is a parallelogram such that Q is the mid-point of EF and  EF = 2HE. Find ∠HQG
  • (i)
    92°
  • (ii)
    90°
  • (iii)
    88°
  • (iv)
    91°
  • (v)
    89°
    Assignment Key
  •  1) (iii)
  •  2) (iv)
  •  3) (i)
  •  4) (iv)
  •  5) (i)
  •  6) (i)
  •  7) (iii)
  •  8) (ii)
  •  9) (ii)
  •  10) (i)
  •  11) (ii)
  •  12) (ii)
  •  13) (ii)
  •  14) (i)
  •  15) (i)
  •  16) (iv)
  •  17) (i)
  •  18) (iii)
  •  19) (iii)
  •  20) (ii)
  •  21) (v)
  •  22) (iii)
  •  23) (iv)
  •  24) (v)
  •  25) (iv)
  •  26) (v)
  •  27) (iv)
  •  28) (v)
  •  29) (i)
  •  30) (i)
  •  31) (iv)
  •  32) (ii)
  •  33) (i)
  •  34) (i)
  •  35) (ii)
  •  36) (iii)
  •  37) (iii)
  •  38) (i)
  •  39) (iii)
  •  40) (iv)
  •  41) (ii)
  •  42) (i)
  •  43) (iv)
  •  44) (iv)
  •  45) (v)
  •  46) (iv)
  •  47) (ii)