EduSahara™ Assignment
Name : Quadrilateral Angle Properties
Chapter : Quadrilaterals
Grade : ICSE Grade VII
License : Non Commercial Use
Question 1
1.
In parallelogram ABCD, if ∠D = 94.38°, then find the value of ∠B
  • (i)
    95.38°
  • (ii)
    93.38°
  • (iii)
    94.38°
  • (iv)
    96.38°
  • (v)
    92.38°
Question 2
2.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
  • (i)
    90°
  • (ii)
    92°
  • (iii)
    89°
  • (iv)
    91°
  • (v)
    88°
Question 3
3.
The sum of the interior angles of a quadrilateral is
  • (i)
    270°
  • (ii)
    180°
  • (iii)
    360°
  • (iv)
    90°
Question 4
4.
If ABCD is an isosceles trapezium, ∠D =
  • (i)
    ∠C
  • (ii)
    ∠B
  • (iii)
    ∠A
  • (iv)
    90°
Question 5
5.
OPQR is a rhombus in which ∠O = 120° .
 

PR
 
 
is the diagonal. Then △OPQ is
  • (i)
    None of these
  • (ii)
    an isosceles triangle
  • (iii)
    a scalene triangle
  • (iv)
    an obtuse angled triangle
  • (v)
    an equilateral triangle
Question 6
6.
DEFG is a rhombus in which ∠D = 108° .
 

EG
 
 
is the diagonal. Then △DEF is
  • (i)
    an isosceles triangle
  • (ii)
    an equilateral triangle
  • (iii)
    a scalene triangle
  • (iv)
    None of these
  • (v)
    an obtuse angled triangle
Question 7
7.
The angles of a quadrilateral HIJK are in the ratio 6 : 4 : 5 : 9. Find the measure of each angle of the quadrilateral.
  • (i)
    H
    =
    89°
    ,
    I
    =
    58°
    ,
    J
    =
    76°
    ,
    K
    =
    137°
  • (ii)
    H
    =
    88°
    ,
    I
    =
    62°
    ,
    J
    =
    74°
    ,
    K
    =
    136°
  • (iii)
    H
    =
    91°
    ,
    I
    =
    59°
    ,
    J
    =
    77°
    ,
    K
    =
    133°
  • (iv)
    H
    =
    90°
    ,
    I
    =
    60°
    ,
    J
    =
    75°
    ,
    K
    =
    135°
  • (v)
    H
    =
    92°
    ,
    I
    =
    59°
    ,
    J
    =
    73°
    ,
    K
    =
    136°
Question 8
8.
Two adjacent angles of a parallelogram ABCD are in the ratio 6 : 12. Find the measure of each of its angles.
  • (i)
    A
    =
    61°
    ,
    B
    =
    119°
    ,
    C
    =
    62°
    ,
    D
    =
    118°
  • (ii)
    A
    =
    62°
    ,
    B
    =
    119°
    ,
    C
    =
    58°
    ,
    D
    =
    121°
  • (iii)
    A
    =
    59°
    ,
    B
    =
    118°
    ,
    C
    =
    61°
    ,
    D
    =
    122°
  • (iv)
    A
    =
    58°
    ,
    B
    =
    122°
    ,
    C
    =
    59°
    ,
    D
    =
    121°
  • (v)
    A
    =
    60°
    ,
    B
    =
    120°
    ,
    C
    =
    60°
    ,
    D
    =
    120°
Question 9
9.
    • In the adjoining figure,
    • OPQR
    • is a parallelogram in which
    • ∠ROQ = 25.6°
    • ,
    • ∠QOP = 55.34°
    • ,
    • ∠RSQ = 55.08°
    • . Calculate
    • ∠OPR
  • (i)
    67.58°
  • (ii)
    71.58°
  • (iii)
    69.58°
  • (iv)
    68.58°
  • (v)
    70.58°
Question 10
10.
    • In the adjoining figure,
    • IJKL
    • is a parallelogram in which
    • ∠LIK = 20.41°
    • ,
    • ∠KIJ = 25.94°
    • ,
    • ∠LMK = 72.69°
    • . Calculate
    • ∠KLJ
  • (i)
    83.37°
  • (ii)
    81.37°
  • (iii)
    82.37°
  • (iv)
    80.37°
  • (v)
    79.37°
Question 11
11.
    • In the adjoining figure,
    • GHIJ
    • is a parallelogram in which
    • ∠JGI = 26.71°
    • ,
    • ∠IGH = 21.09°
    • ,
    • ∠JKI = 106.98°
    • . Calculate
    • ∠HIG
  • (i)
    28.71°
  • (ii)
    25.71°
  • (iii)
    26.71°
  • (iv)
    24.71°
  • (v)
    27.71°
Question 12
12.
    • In the adjoining figure,
    • PQRS
    • is a parallelogram in which
    • ∠SPR = 48.55°
    • ,
    • ∠RPQ = 36.25°
    • ,
    • ∠STR = 103.51°
    • . Calculate
    • ∠SQR
  • (i)
    55.95°
  • (ii)
    53.95°
  • (iii)
    56.95°
  • (iv)
    54.95°
  • (v)
    52.95°
Question 13
13.
    • In the adjoining figure,
    • IJKL
    • is a rectangle.
    • If
    • ∠KIJ = 43.15°
    • , find
    • ∠KMJ
  • (i)
    86.30°
  • (ii)
    88.30°
  • (iii)
    84.30°
  • (iv)
    85.30°
  • (v)
    87.30°
Question 14
14.
Three angles of quadrilateral measure 136.42°, 98.45° and 76.66° respectively. Find the measure of the fourth angle
  • (i)
    46.47°
  • (ii)
    48.47°
  • (iii)
    47.47°
  • (iv)
    49.47°
  • (v)
    50.47°
Question 15
15.
Three angles of a quadrilateral are equal and the fourth angle measure 102.07°. What is the measure of each of the equal angles?
  • (i)
    83.98°
  • (ii)
    87.98°
  • (iii)
    86.98°
  • (iv)
    84.98°
  • (v)
    85.98°
Question 16
16.
Two angles of a quadrilateral are of measure 43.69° and 125.12° respectively and the other two angles are equal. Find the measure of each of the equal angles.
  • (i)
    96.59°
  • (ii)
    97.59°
  • (iii)
    93.59°
  • (iv)
    94.59°
  • (v)
    95.59°
Question 17
17.
A quadrilateral has three acute angles, each measuring 47°. What is the measure of its fourth angle?
  • (i)
    217.00°
  • (ii)
    221.00°
  • (iii)
    220.00°
  • (iv)
    218.00°
  • (v)
    219.00°
Question 18
18.
    • One angle of a parallelogram measures
    • K
    • =
    • 76.87°
    • .
    • Find the measure of each of its remaining angles.
  • (i)
    L
    =
    101.13°
    ,
    M
    =
    74.87°
    ,
    N
    =
    101.13°
  • (ii)
    L
    =
    102.13°
    ,
    M
    =
    75.87°
    ,
    N
    =
    102.13°
  • (iii)
    L
    =
    104.13°
    ,
    M
    =
    77.87°
    ,
    N
    =
    104.13°
  • (iv)
    L
    =
    103.13°
    ,
    M
    =
    76.87°
    ,
    N
    =
    103.13°
  • (v)
    L
    =
    105.13°
    ,
    M
    =
    78.87°
    ,
    N
    =
    105.13°
Question 19
19.
    • Two adjacent angles of a parallelogram are in the ratio
    • 3 : 3
    • .
    • Find the measure of each of its angles.
  • (i)
    A
    =
    91°
    ,
    B
    =
    89°
    ,
    C
    =
    92°
    ,
    D
    =
    88°
  • (ii)
    A
    =
    88°
    ,
    B
    =
    92°
    ,
    C
    =
    89°
    ,
    D
    =
    91°
  • (iii)
    A
    =
    90°
    ,
    B
    =
    90°
    ,
    C
    =
    90°
    ,
    D
    =
    90°
  • (iv)
    A
    =
    92°
    ,
    B
    =
    89°
    ,
    C
    =
    88°
    ,
    D
    =
    91°
  • (v)
    A
    =
    89°
    ,
    B
    =
    88°
    ,
    C
    =
    91°
    ,
    D
    =
    92°
Question 20
20.
    • In the figure given below,
    • KLMN
    • is a rectangle.
    • Find the values of x and y
  • (i)
    x
    =
    47.29°
    ,
    y
    =
    94.58°
  • (ii)
    x
    =
    45.29°
    ,
    y
    =
    92.58°
  • (iii)
    x
    =
    48.29°
    ,
    y
    =
    95.58°
  • (iv)
    x
    =
    46.29°
    ,
    y
    =
    93.58°
  • (v)
    x
    =
    49.29°
    ,
    y
    =
    96.58°
Question 21
21.
    • In the figure given below,
    • MNOP
    • is a rectangle.
    • Find the values of x and y
  • (i)
    x
    =
    41.03°
    ,
    y
    =
    44.97°
  • (ii)
    x
    =
    44.03°
    ,
    y
    =
    47.97°
  • (iii)
    x
    =
    43.03°
    ,
    y
    =
    46.97°
  • (iv)
    x
    =
    42.03°
    ,
    y
    =
    45.97°
  • (v)
    x
    =
    45.03°
    ,
    y
    =
    48.97°
Question 22
22.
    • In the figure given below,
    • HIJK
    • is a rhombus.
    • Find the values of x and y
  • (i)
    x
    =
    28.09°
    ,
    y
    =
    28.09°
  • (ii)
    x
    =
    29.09°
    ,
    y
    =
    29.09°
  • (iii)
    x
    =
    25.09°
    ,
    y
    =
    25.09°
  • (iv)
    x
    =
    27.09°
    ,
    y
    =
    27.09°
  • (v)
    x
    =
    26.09°
    ,
    y
    =
    26.09°
Question 23
23.
    • In the figure given below,
    • FGHI
    • is a rhombus.
    • Find the values of x and y
  • (i)
    x
    =
    32.26°
    ,
    y
    =
    32.26°
  • (ii)
    x
    =
    30.26°
    ,
    y
    =
    30.26°
  • (iii)
    x
    =
    28.26°
    ,
    y
    =
    28.26°
  • (iv)
    x
    =
    29.26°
    ,
    y
    =
    29.26°
  • (v)
    x
    =
    31.26°
    ,
    y
    =
    31.26°
Question 24
24.
    • In the figure given below,
    • DEFG
    • is a rhombus.
    • Find the values of x and y
  • (i)
    x
    =
    17.92°
    ,
    y
    =
    76.08°
  • (ii)
    x
    =
    16.92°
    ,
    y
    =
    75.08°
  • (iii)
    x
    =
    14.92°
    ,
    y
    =
    73.08°
  • (iv)
    x
    =
    15.92°
    ,
    y
    =
    74.08°
  • (v)
    x
    =
    13.92°
    ,
    y
    =
    72.08°
Question 25
25.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
  • (i)
    K
    =
    61°
    ,
    L
    =
    119°
    ,
    M
    =
    62°
    ,
    N
    =
    118°
  • (ii)
    K
    =
    60°
    ,
    L
    =
    120°
    ,
    M
    =
    60°
    ,
    N
    =
    120°
  • (iii)
    K
    =
    58°
    ,
    L
    =
    122°
    ,
    M
    =
    59°
    ,
    N
    =
    121°
  • (iv)
    K
    =
    62°
    ,
    L
    =
    119°
    ,
    M
    =
    58°
    ,
    N
    =
    121°
  • (v)
    K
    =
    59°
    ,
    L
    =
    118°
    ,
    M
    =
    61°
    ,
    N
    =
    122°
Question 26
26.
    • In the adjoining figure,
    • ABCD
    • is a trapezium in which
    •  

      AB
       
       
      ∥
       

      CD
       
       
    • .
    • If
    •  
    • x = 110.08°
    • and
    •  
    • y = 111.16°
    • ,
    • find the measures of
    • ∠A
    • and
    • ∠B
    • .
  • (i)
    A
    =
    69.84°
    ,
    B
    =
    70.92°
  • (ii)
    A
    =
    67.84°
    ,
    B
    =
    68.92°
  • (iii)
    A
    =
    66.84°
    ,
    B
    =
    67.92°
  • (iv)
    A
    =
    68.84°
    ,
    B
    =
    69.92°
  • (v)
    A
    =
    70.84°
    ,
    B
    =
    71.92°
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 = 34.43° and ∠ABO = 58.37°, find the measure of each of the angles marked a,b,c,d and e.
  • (i)
    a = 55.57° , b = 31.63° , c = 58.37° , d = 55.57° , e = 34.43°
  • (ii)
    a = 55.57° , b = 32.63° , c = 57.37° , d = 55.57° , e = 34.43°
  • (iii)
    a = 55.57° , b = 32.63° , c = 57.37° , d = 57.57° , e = 34.43°
  • (iv)
    a = 55.57° , b = 32.63° , c = 57.37° , d = 57.57° , e = 32.43°
  • (v)
    a = 55.57° , b = 32.63° , c = 58.37° , d = 55.57° , e = 34.43°
Question 28
28.
    • In the adjoining figure,
    • ABCD
    • is a rhombus whose diagonals intersect at
    • O
    • .
    • If
    • ∠OAB
    • :
    • ∠ABO
    • =
    • 5 : 13
    • ,
    • find the angles of
    • △OAB
    • .
  • (i)
    O
    =
    90°
    ,
    A
    =
    25°
    ,
    B
    =
    65°
  • (ii)
    O
    =
    90°
    ,
    A
    =
    23°
    ,
    B
    =
    67°
  • (iii)
    O
    =
    88°
    ,
    A
    =
    27°
    ,
    B
    =
    65°
  • (iv)
    O
    =
    88°
    ,
    A
    =
    25°
    ,
    B
    =
    67°
  • (v)
    O
    =
    92°
    ,
    A
    =
    25°
    ,
    B
    =
    63°
Question 29
29.
    • The measures of three angles of a quadrilateral are
    • 66.42°
    • ,
    • 104.72°
    • and
    • 76.87°
    • . Find the fourth angle
  • (i)
    111.99°
  • (ii)
    116.99°
  • (iii)
    121.99°
  • (iv)
    141.99°
  • (v)
    126.99°
Question 30
30.
Find the missing angle in the given quadrilateral
  • (i)
    145.6°
  • (ii)
    115.6°
  • (iii)
    125.6°
  • (iv)
    120.6°
  • (v)
    130.6°
Question 31
31.
Find the missing angle in the given trapezium
  • (i)
    130.42°
  • (ii)
    155.42°
  • (iii)
    125.42°
  • (iv)
    135.42°
  • (v)
    140.42°
Question 32
32.
Find the missing angle in the given parallelogram
  • (i)
    141.02°
  • (ii)
    116.02°
  • (iii)
    111.02°
  • (iv)
    126.02°
  • (v)
    121.02°
Question 33
33.
Find the missing angle in the given rhombus
  • (i)
    61.7°
  • (ii)
    76.7°
  • (iii)
    51.7°
  • (iv)
    46.7°
  • (v)
    56.7°
Question 34
34.
    • In the adjoining figure,
    • PQRS
    • is a parallelogram and
    • TU
    • is such that
    •  

      TU
       
       
      ∥
       

      PR
       
       
    • If
    • ∠PST = 44.81°
    • and
    • ∠RSU = 41.82°
    • ,
    • find the measure of
    • ∠PQR
    • .
  • (i)
    94.37°
  • (ii)
    91.37°
  • (iii)
    92.37°
  • (iv)
    95.37°
  • (v)
    93.37°
Question 35
35.
In the adjoining figure, LMNO is a square. A line segment OQ cuts the side MN at Q and the diagonal LN at P such that ∠OPN = 109.62° and ∠PQN = x°. Find the value of x .
  • (i)
    66.62°
  • (ii)
    62.62°
  • (iii)
    63.62°
  • (iv)
    64.62°
  • (v)
    65.62°
Question 36
36.
In the adjoining figure, MNOP is a rhombus and △QPO is an equilateral triangle. Q and N are on opposite sides of  OP. If ∠PMN = 68.4°, find the values of  x  and  y .
  • (i)
    x
    =
    28°
    ,
    y
    =
    23.8°
  • (ii)
    x
    =
    31°
    ,
    y
    =
    26.8°
  • (iii)
    x
    =
    32°
    ,
    y
    =
    27.8°
  • (iv)
    x
    =
    30°
    ,
    y
    =
    25.8°
  • (v)
    x
    =
    29°
    ,
    y
    =
    24.8°
Question 37
37.
In the adjoining figure, equilateral  △MLN surmounts square  JKLM. If  LNK = x°, find the value of x.
  • (i)
    15°
  • (ii)
    16°
  • (iii)
    13°
  • (iv)
    14°
  • (v)
    17°
Question 38
38.
    • In the given figure,
    • PQRS
    • is a rectangle whose diagonals intersect at
    • T
    • .
    • Diagonal
    • PR
    • is produced to
    • T
    • and
    • ∠SRT =
    • 129.81°
    • . Find the angles of
    • △TQR
    • .
  • (i)
    T
    =
    98.38°
    ,
    Q
    =
    41.81°
    ,
    R
    =
    39.81°
  • (ii)
    T
    =
    100.38°
    ,
    Q
    =
    39.81°
    ,
    R
    =
    39.81°
  • (iii)
    T
    =
    98.38°
    ,
    Q
    =
    39.81°
    ,
    R
    =
    41.81°
  • (iv)
    T
    =
    102.38°
    ,
    Q
    =
    39.81°
    ,
    R
    =
    37.81°
  • (v)
    T
    =
    100.38°
    ,
    Q
    =
    37.81°
    ,
    R
    =
    41.81°
Question 39
39.
    • In the given figure,
    • PQRS
    • is a kite whose diagonals intersect at
    • T
    • .
    • If
    • ∠QRS = 113.15°
    • and
    • ∠RSP = 74.77°
    • , calculate
    • ∠TPQ
    • and
    • ∠RTQ
    • .
  • (i)
    x
    =
    47.66°
    ,
    y
    =
    89°
  • (ii)
    x
    =
    49.66°
    ,
    y
    =
    91°
  • (iii)
    x
    =
    46.66°
    ,
    y
    =
    88°
  • (iv)
    x
    =
    48.66°
    ,
    y
    =
    90°
  • (v)
    x
    =
    50.66°
    ,
    y
    =
    92°
Question 40
40.
    • △KJG
    • is an equilateral triangle in a square
    • GHIJ
    • .
    • If
    • GI
    • and
    • KJ
    • intersect at
    • L
    • ,
    • 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 = 57°
    • ,
    • find the measure of x .
  • (i)
    124°
  • (ii)
    125°
  • (iii)
    122°
  • (iv)
    121°
  • (v)
    123°
Question 42
42.
    • In the given figure, FGHI is a parallelogram. Q is the mid-point of HI.
    • GQ
    • bisects
    • ∠G
    • . If x =
    • 52°
    • , find angle 'y'.
  • (i)
    40°
  • (ii)
    36°
  • (iii)
    38°
  • (iv)
    39°
  • (v)
    37°
Question 43
43.
In the given figure, FGHI is a rhombus. Given x = 58°, find the value of 'y'.
  • (i)
    33°
  • (ii)
    32°
  • (iii)
    34°
  • (iv)
    30°
  • (v)
    31°
Question 44
44.
    • In the given figure, CDEF is a parallelogram. DF is the diagonal
    • such that
    •  
    • CF = DF = DE
    • . Given
    • ∠C = 60°
    • , find
    • ∠FDE
  • (i)
    59°
  • (ii)
    60°
  • (iii)
    58°
  • (iv)
    62°
  • (v)
    61°
Question 45
45.
In the given figure, HIJK is a parallelogram. HS and JT are perpendicular to the diagonal IK. Given ∠SHI = 29°, find ∠JKI
  • (i)
    61°
  • (ii)
    63°
  • (iii)
    59°
  • (iv)
    60°
  • (v)
    62°
Question 46
46.
In the given figure, DEFG is a rhombus such that ∠E = 120°. Then △DEG is
  • (i)
    Equilateral triangle
  • (ii)
    Isosceles triangle
  • (iii)
    Right angled triangle
  • (iv)
    Obtuse angled 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)
    91°
  • (ii)
    88°
  • (iii)
    89°
  • (iv)
    90°
  • (v)
    92°
    Assignment Key
  •  1) (iii)
  •  2) (i)
  •  3) (iii)
  •  4) (i)
  •  5) (v)
  •  6) (i)
  •  7) (iv)
  •  8) (v)
  •  9) (iii)
  •  10) (ii)
  •  11) (iii)
  •  12) (iv)
  •  13) (i)
  •  14) (ii)
  •  15) (v)
  •  16) (v)
  •  17) (v)
  •  18) (iv)
  •  19) (iii)
  •  20) (i)
  •  21) (iii)
  •  22) (iv)
  •  23) (ii)
  •  24) (iv)
  •  25) (ii)
  •  26) (iv)
  •  27) (i)
  •  28) (i)
  •  29) (i)
  •  30) (ii)
  •  31) (iii)
  •  32) (iii)
  •  33) (iv)
  •  34) (v)
  •  35) (iv)
  •  36) (iv)
  •  37) (i)
  •  38) (ii)
  •  39) (iv)
  •  40) (iv)
  •  41) (v)
  •  42) (iii)
  •  43) (ii)
  •  44) (ii)
  •  45) (i)
  •  46) (i)
  •  47) (iv)