EduSahara™ Assignment
Name : Quadrilateral Angle Problems
Chapter : Quadrilaterals
Grade : SSC Grade VII
License : Non Commercial Use
Question 1
1.
    • The measures of three angles of a quadrilateral are
    • 72.62°
    • ,
    • 83.36°
    • and
    • 70.53°
    • . Find the fourth angle
  • (i)
    138.49°
  • (ii)
    148.49°
  • (iii)
    163.49°
  • (iv)
    143.49°
  • (v)
    133.49°
Question 2
2.
Find the missing angle in the given quadrilateral
  • (i)
    82.61°
  • (ii)
    72.61°
  • (iii)
    67.61°
  • (iv)
    97.61°
  • (v)
    77.61°
Question 3
3.
Find the missing angle in the given trapezium
  • (i)
    104.46°
  • (ii)
    109.46°
  • (iii)
    114.46°
  • (iv)
    129.46°
  • (v)
    99.46°
Question 4
4.
Find the missing angle in the given rhombus
  • (i)
    93.47°
  • (ii)
    108.47°
  • (iii)
    83.47°
  • (iv)
    78.47°
  • (v)
    88.47°
Question 5
5.
In parallelogram ABCD, if ∠D = 113.99°, then find the value of ∠C
  • (i)
    66.01°
  • (ii)
    67.01°
  • (iii)
    65.01°
  • (iv)
    64.01°
  • (v)
    68.01°
Question 6
6.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
  • (i)
    88°
  • (ii)
    91°
  • (iii)
    89°
  • (iv)
    90°
  • (v)
    92°
Question 7
7.
The sum of the interior angles of a quadrilateral is
  • (i)
    270°
  • (ii)
    360°
  • (iii)
    180°
  • (iv)
    90°
Question 8
8.
If ABCD is an isosceles trapezium, ∠C =
  • (i)
    ∠D
  • (ii)
    90°
  • (iii)
    ∠A
  • (iv)
    ∠B
Question 9
9.
FGHI is a rhombus in which ∠F = 120° .
 

GI
 
 
is the diagonal. Then △FGH is
  • (i)
    a scalene triangle
  • (ii)
    an equilateral triangle
  • (iii)
    an obtuse angled triangle
  • (iv)
    an isosceles triangle
  • (v)
    None of these
Question 10
10.
NOPQ is a rhombus in which ∠N = 90° .
 

OQ
 
 
is the diagonal. Then △NOP is
  • (i)
    an obtuse angled triangle
  • (ii)
    an equilateral triangle
  • (iii)
    an isosceles triangle
  • (iv)
    a scalene triangle
  • (v)
    None of these
Question 11
11.
The angles of a quadrilateral PQRS are in the ratio 1 : 2 : 3 : 6. Find the measure of each angle of the quadrilateral.
  • (i)
    P
    =
    31°
    ,
    Q
    =
    59°
    ,
    R
    =
    92°
    ,
    S
    =
    178°
  • (ii)
    P
    =
    29°
    ,
    Q
    =
    58°
    ,
    R
    =
    91°
    ,
    S
    =
    182°
  • (iii)
    P
    =
    30°
    ,
    Q
    =
    60°
    ,
    R
    =
    90°
    ,
    S
    =
    180°
  • (iv)
    P
    =
    32°
    ,
    Q
    =
    59°
    ,
    R
    =
    88°
    ,
    S
    =
    181°
  • (v)
    P
    =
    28°
    ,
    Q
    =
    62°
    ,
    R
    =
    89°
    ,
    S
    =
    181°
Question 12
12.
Two adjacent angles of a parallelogram KLMN are in the ratio 13 : 77. Find the measure of each of its angles.
  • (i)
    K
    =
    28°
    ,
    L
    =
    153°
    ,
    M
    =
    24°
    ,
    N
    =
    155°
  • (ii)
    K
    =
    26°
    ,
    L
    =
    154°
    ,
    M
    =
    26°
    ,
    N
    =
    154°
  • (iii)
    K
    =
    24°
    ,
    L
    =
    156°
    ,
    M
    =
    25°
    ,
    N
    =
    155°
  • (iv)
    K
    =
    27°
    ,
    L
    =
    153°
    ,
    M
    =
    28°
    ,
    N
    =
    152°
  • (v)
    K
    =
    25°
    ,
    L
    =
    152°
    ,
    M
    =
    27°
    ,
    N
    =
    156°
Question 13
13.
    • In the adjoining figure,
    • EFGH
    • is a parallelogram in which
    • ∠HEG = 51.61°
    • ,
    • ∠GEF = 41.26°
    • ,
    • ∠HIG = 100.35°
    • . Calculate
    • ∠EFH
  • (i)
    37.39°
  • (ii)
    38.39°
  • (iii)
    40.39°
  • (iv)
    36.39°
  • (v)
    39.39°
Question 14
14.
    • In the adjoining figure,
    • KLMN
    • is a parallelogram in which
    • ∠NKM = 26.58°
    • ,
    • ∠MKL = 22.09°
    • ,
    • ∠NOM = 101.31°
    • . Calculate
    • ∠MNL
  • (i)
    56.60°
  • (ii)
    57.60°
  • (iii)
    58.60°
  • (iv)
    54.60°
  • (v)
    55.60°
Question 15
15.
Three angles of quadrilateral measure 65.09°, 118° and 106.07° respectively. Find the measure of the fourth angle
  • (i)
    69.84°
  • (ii)
    71.84°
  • (iii)
    68.84°
  • (iv)
    70.84°
  • (v)
    72.84°
Question 16
16.
Three angles of a quadrilateral are equal and the fourth angle measure 76.33°. What is the measure of each of the equal angles?
  • (i)
    92.56°
  • (ii)
    96.56°
  • (iii)
    95.56°
  • (iv)
    93.56°
  • (v)
    94.56°
Question 17
17.
Two angles of a quadrilateral are of measure 90° and 89.71° respectively and the other two angles are equal. Find the measure of each of the equal angles.
  • (i)
    89.15°
  • (ii)
    88.15°
  • (iii)
    91.15°
  • (iv)
    90.15°
  • (v)
    92.15°
Question 18
18.
A quadrilateral has three acute angles, each measuring 40°. What is the measure of its fourth angle?
  • (i)
    239.00°
  • (ii)
    240.00°
  • (iii)
    238.00°
  • (iv)
    241.00°
  • (v)
    242.00°
Question 19
19.
    • One angle of a parallelogram measures
    • P
    • =
    • 51.32°
    • .
    • Find the measure of each of its remaining angles.
  • (i)
    Q
    =
    129.68°
    ,
    R
    =
    52.32°
    ,
    S
    =
    129.68°
  • (ii)
    Q
    =
    130.68°
    ,
    R
    =
    53.32°
    ,
    S
    =
    130.68°
  • (iii)
    Q
    =
    127.68°
    ,
    R
    =
    50.32°
    ,
    S
    =
    127.68°
  • (iv)
    Q
    =
    126.68°
    ,
    R
    =
    49.32°
    ,
    S
    =
    126.68°
  • (v)
    Q
    =
    128.68°
    ,
    R
    =
    51.32°
    ,
    S
    =
    128.68°
Question 20
20.
    • Two adjacent angles of a parallelogram are in the ratio
    • 3 : 15
    • .
    • Find the measure of each of its angles.
  • (i)
    A
    =
    28°
    ,
    B
    =
    152°
    ,
    C
    =
    29°
    ,
    D
    =
    151°
  • (ii)
    A
    =
    29°
    ,
    B
    =
    148°
    ,
    C
    =
    31°
    ,
    D
    =
    152°
  • (iii)
    A
    =
    30°
    ,
    B
    =
    150°
    ,
    C
    =
    30°
    ,
    D
    =
    150°
  • (iv)
    A
    =
    31°
    ,
    B
    =
    149°
    ,
    C
    =
    32°
    ,
    D
    =
    148°
  • (v)
    A
    =
    32°
    ,
    B
    =
    149°
    ,
    C
    =
    28°
    ,
    D
    =
    151°
Question 21
21.
    • In the figure given below,
    • JKLM
    • is a rhombus.
    • Find the values of x and y
  • (i)
    x
    =
    32.51°
    ,
    y
    =
    32.51°
  • (ii)
    x
    =
    31.51°
    ,
    y
    =
    31.51°
  • (iii)
    x
    =
    33.51°
    ,
    y
    =
    33.51°
  • (iv)
    x
    =
    30.51°
    ,
    y
    =
    30.51°
  • (v)
    x
    =
    34.51°
    ,
    y
    =
    34.51°
Question 22
22.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
  • (i)
    A
    =
    60°
    ,
    B
    =
    120°
    ,
    C
    =
    60°
    ,
    D
    =
    120°
  • (ii)
    A
    =
    61°
    ,
    B
    =
    119°
    ,
    C
    =
    62°
    ,
    D
    =
    118°
  • (iii)
    A
    =
    59°
    ,
    B
    =
    118°
    ,
    C
    =
    61°
    ,
    D
    =
    122°
  • (iv)
    A
    =
    62°
    ,
    B
    =
    119°
    ,
    C
    =
    58°
    ,
    D
    =
    121°
  • (v)
    A
    =
    58°
    ,
    B
    =
    122°
    ,
    C
    =
    59°
    ,
    D
    =
    121°
Question 23
23.
    • In the adjoining figure,
    • FGHI
    • is a trapezium in which
    •  

      FG
       
       
      ∥
       

      HI
       
       
    • .
    • If
    •  
    • x = 47.49°
    • and
    •  
    • y = 77.09°
    • ,
    • find the measures of
    • ∠H
    • and
    • ∠I
    • .
  • (i)
    H
    =
    101.91°
    ,
    I
    =
    131.51°
  • (ii)
    H
    =
    103.91°
    ,
    I
    =
    133.51°
  • (iii)
    H
    =
    100.91°
    ,
    I
    =
    130.51°
  • (iv)
    H
    =
    102.91°
    ,
    I
    =
    132.51°
  • (v)
    H
    =
    104.91°
    ,
    I
    =
    134.51°
Question 24
24.
    • 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
    =
    90°
    ,
    A
    =
    36°
    ,
    B
    =
    54°
  • (iii)
    O
    =
    90°
    ,
    A
    =
    34°
    ,
    B
    =
    56°
  • (iv)
    O
    =
    92°
    ,
    A
    =
    36°
    ,
    B
    =
    52°
  • (v)
    O
    =
    88°
    ,
    A
    =
    38°
    ,
    B
    =
    54°
Question 25
25.
Find the missing angle in the given parallelogram
  • (i)
    155.1°
  • (ii)
    140.1°
  • (iii)
    125.1°
  • (iv)
    135.1°
  • (v)
    130.1°
Question 26
26.
    • In the adjoining figure,
    • HIJK
    • is a parallelogram in which
    • ∠KHJ = 8.28°
    • ,
    • ∠JHI = 13.95°
    • ,
    • ∠KLJ = 35.08°
    • . Calculate
    • ∠IJH
  • (i)
    6.28°
  • (ii)
    9.28°
  • (iii)
    8.28°
  • (iv)
    10.28°
  • (v)
    7.28°
Question 27
27.
    • In the adjoining figure,
    • JKLM
    • is a parallelogram in which
    • ∠MJL = 25.15°
    • ,
    • ∠LJK = 40.55°
    • ,
    • ∠MNL = 63.46°
    • . Calculate
    • ∠MKL
  • (i)
    39.31°
  • (ii)
    36.31°
  • (iii)
    38.31°
  • (iv)
    40.31°
  • (v)
    37.31°
Question 28
28.
    • In the adjoining figure,
    • HIJK
    • is a rectangle.
    • If
    • ∠JHI = 48.37°
    • , find
    • ∠HIK
  • (i)
    46.37°
  • (ii)
    48.37°
  • (iii)
    47.37°
  • (iv)
    50.37°
  • (v)
    49.37°
Question 29
29.
    • In the figure given below,
    • KLMN
    • is a rectangle.
    • Find the values of x and y
  • (i)
    x
    =
    44.55°
    ,
    y
    =
    91.1°
  • (ii)
    x
    =
    46.55°
    ,
    y
    =
    93.1°
  • (iii)
    x
    =
    47.55°
    ,
    y
    =
    94.1°
  • (iv)
    x
    =
    45.55°
    ,
    y
    =
    92.1°
  • (v)
    x
    =
    48.55°
    ,
    y
    =
    95.1°
Question 30
30.
    • In the figure given below,
    • PQRS
    • is a rectangle.
    • Find the values of x and y
  • (i)
    x
    =
    47.76°
    ,
    y
    =
    38.24°
  • (ii)
    x
    =
    51.76°
    ,
    y
    =
    42.24°
  • (iii)
    x
    =
    50.76°
    ,
    y
    =
    41.24°
  • (iv)
    x
    =
    49.76°
    ,
    y
    =
    40.24°
  • (v)
    x
    =
    48.76°
    ,
    y
    =
    39.24°
Question 31
31.
    • In the figure given below,
    • NOPQ
    • is a rhombus.
    • Find the values of x and y
  • (i)
    x
    =
    67.86°
    ,
    y
    =
    67.86°
  • (ii)
    x
    =
    69.86°
    ,
    y
    =
    69.86°
  • (iii)
    x
    =
    70.86°
    ,
    y
    =
    70.86°
  • (iv)
    x
    =
    68.86°
    ,
    y
    =
    68.86°
  • (v)
    x
    =
    66.86°
    ,
    y
    =
    66.86°
Question 32
32.
    • In the figure given below,
    • BCDE
    • is a rhombus.
    • Find the values of x and y
  • (i)
    x
    =
    48.31°
    ,
    y
    =
    41.69°
  • (ii)
    x
    =
    47.31°
    ,
    y
    =
    40.69°
  • (iii)
    x
    =
    46.31°
    ,
    y
    =
    39.69°
  • (iv)
    x
    =
    49.31°
    ,
    y
    =
    42.69°
  • (v)
    x
    =
    50.31°
    ,
    y
    =
    43.69°
Question 33
33.
    • 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 = 36.65° and ∠ABO = 40.03°, find the measure of each of the angles marked a,b,c,d and e.
  • (i)
    a = 53.35° , b = 50.97° , c = 39.03° , d = 55.35° , e = 34.65°
  • (ii)
    a = 53.35° , b = 50.97° , c = 39.03° , d = 55.35° , e = 36.65°
  • (iii)
    a = 53.35° , b = 50.97° , c = 39.03° , d = 53.35° , e = 36.65°
  • (iv)
    a = 53.35° , b = 50.97° , c = 40.03° , d = 53.35° , e = 36.65°
  • (v)
    a = 53.35° , b = 49.97° , c = 40.03° , d = 53.35° , e = 36.65°
Question 34
34.
In the adjoining figure, side HI of parallelogram GHIJ has been produced to K. If ∠GHK = 59.28° , find the measure of each angle of the parallelogram.
  • (i)
    G
    =
    61.28°
    ,
    H
    =
    119.72°
    ,
    I
    =
    57.28°
    ,
    J
    =
    121.72°
  • (ii)
    G
    =
    58.28°
    ,
    H
    =
    118.72°
    ,
    I
    =
    60.28°
    ,
    J
    =
    122.72°
  • (iii)
    G
    =
    60.28°
    ,
    H
    =
    119.72°
    ,
    I
    =
    61.28°
    ,
    J
    =
    118.72°
  • (iv)
    G
    =
    59.28°
    ,
    H
    =
    120.72°
    ,
    I
    =
    59.28°
    ,
    J
    =
    120.72°
  • (v)
    G
    =
    57.28°
    ,
    H
    =
    122.72°
    ,
    I
    =
    58.28°
    ,
    J
    =
    121.72°
Question 35
35.
    • In the adjoining figure,
    • DEFG
    • is a parallelogram and
    • HI
    • is such that
    •  

      HI
       
       
      ∥
       

      DF
       
       
    • If
    • ∠DGH = 32.29°
    • and
    • ∠FGI = 40.22°
    • ,
    • find the measure of
    • ∠FGD
    • .
  • (i)
    105.49°
  • (ii)
    109.49°
  • (iii)
    106.49°
  • (iv)
    108.49°
  • (v)
    107.49°
Question 36
36.
In the adjoining figure, EFGH is a square. A line segment HJ cuts the side FG at J and the diagonal EG at I such that ∠HIG = 106.45° and ∠IJG = x°. Find the value of x .
  • (i)
    63.45°
  • (ii)
    61.45°
  • (iii)
    62.45°
  • (iv)
    60.45°
  • (v)
    59.45°
Question 37
37.
In the adjoining figure, GHIJ is a rhombus and △KJI is an equilateral triangle. K and H are on opposite sides of  IJ. If ∠JGH = 38.91°, find the values of  x  and  y .
  • (i)
    x
    =
    28°
    ,
    y
    =
    38.55°
  • (ii)
    x
    =
    32°
    ,
    y
    =
    42.55°
  • (iii)
    x
    =
    31°
    ,
    y
    =
    41.55°
  • (iv)
    x
    =
    29°
    ,
    y
    =
    39.55°
  • (v)
    x
    =
    30°
    ,
    y
    =
    40.55°
Question 38
38.
In the adjoining figure, equilateral  △IHJ surmounts square  FGHI. If  HJF = x°, find the value of x.
  • (i)
    47°
  • (ii)
    46°
  • (iii)
    45°
  • (iv)
    43°
  • (v)
    44°
Question 39
39.
    • In the given figure,
    • PQRS
    • is a rectangle whose diagonals intersect at
    • T
    • .
    • Diagonal
    • PR
    • is produced to
    • T
    • and
    • ∠SRT =
    • 140.53°
    • . Find the angles of
    • △TPQ
    • .
  • (i)
    T
    =
    99.06°
    ,
    P
    =
    39.47°
    ,
    Q
    =
    41.47°
  • (ii)
    T
    =
    101.06°
    ,
    P
    =
    39.47°
    ,
    Q
    =
    39.47°
  • (iii)
    T
    =
    103.06°
    ,
    P
    =
    39.47°
    ,
    Q
    =
    37.47°
  • (iv)
    T
    =
    101.06°
    ,
    P
    =
    37.47°
    ,
    Q
    =
    41.47°
  • (v)
    T
    =
    99.06°
    ,
    P
    =
    41.47°
    ,
    Q
    =
    39.47°
Question 40
40.
    • In the given figure,
    • JKLM
    • is a kite whose diagonals intersect at
    • N
    • .
    • If
    • ∠MJK = 65.74°
    • and
    • ∠JKL = 100.26°
    • , calculate
    • ∠NMJ
    • and
    • ∠NLM
    • .
  • (i)
    x
    =
    56.13°
    ,
    y
    =
    45.87°
  • (ii)
    x
    =
    57.13°
    ,
    y
    =
    46.87°
  • (iii)
    x
    =
    58.13°
    ,
    y
    =
    47.87°
  • (iv)
    x
    =
    55.13°
    ,
    y
    =
    44.87°
  • (v)
    x
    =
    59.13°
    ,
    y
    =
    48.87°
Question 41
41.
    • △HEF
    • is an equilateral triangle in a square
    • DEFG
    • .
    • If
    • DF
    • and
    • HE
    • intersect at
    • I
    • ,
    • then find the value of x.
  • (i)
    74°
  • (ii)
    75°
  • (iii)
    76°
  • (iv)
    73°
  • (v)
    77°
Question 42
42.
    • In the adjoining figure,
    • J
    • is a point in the interior of
    • ∠LHM
    • .
    • If
    •  
    • JI
    • ⟂
    • HL
    • and
    • JK
    • ⟂
    • HM
    • and
    • ∠LHM = 59°
    • ,
    • find the measure of x .
  • (i)
    238°
  • (ii)
    240°
  • (iii)
    241°
  • (iv)
    239°
  • (v)
    237°
Question 43
43.
In the given figure, HIJK is a rhombus. Given x = 51°, find the value of 'y'.
  • (i)
    39°
  • (ii)
    40°
  • (iii)
    37°
  • (iv)
    41°
  • (v)
    38°
Question 44
44.
    • In the given figure, EFGH is a parallelogram. EG bisects ∠E & ∠G.
    • Given
    • EG = 12 cm
    • and
    • FH = 8 cm
    • , find
    • EF
  • (i)
    8.21 cm
  • (ii)
    5.21 cm
  • (iii)
    9.21 cm
  • (iv)
    6.21 cm
  • (v)
    7.21 cm
Question 45
45.
    • In the given figure, CDEF is a parallelogram. DF is the diagonal
    • such that
    •  
    • CF = DF = DE
    • . Given
    • ∠C = 52°
    • , find
    • ∠FDE
  • (i)
    76°
  • (ii)
    78°
  • (iii)
    74°
  • (iv)
    75°
  • (v)
    77°
Question 46
46.
In the given figure, BCDE is a parallelogram. BR and DS are perpendicular to the diagonal CE. Given ∠RBC = 41°, find ∠DEC
  • (i)
    49°
  • (ii)
    51°
  • (iii)
    48°
  • (iv)
    50°
  • (v)
    47°
Question 47
47.
In the given figure, EFGH is a rhombus such that ∠F = 120°. Then △EFH is
  • (i)
    Obtuse angled triangle
  • (ii)
    Isosceles triangle
  • (iii)
    Equilateral triangle
  • (iv)
    Right angled triangle
    Assignment Key
  •  1) (v)
  •  2) (iii)
  •  3) (v)
  •  4) (iv)
  •  5) (i)
  •  6) (iv)
  •  7) (ii)
  •  8) (i)
  •  9) (ii)
  •  10) (iii)
  •  11) (iii)
  •  12) (ii)
  •  13) (ii)
  •  14) (i)
  •  15) (iv)
  •  16) (v)
  •  17) (iv)
  •  18) (ii)
  •  19) (v)
  •  20) (iii)
  •  21) (i)
  •  22) (i)
  •  23) (iv)
  •  24) (ii)
  •  25) (iii)
  •  26) (iii)
  •  27) (iii)
  •  28) (ii)
  •  29) (ii)
  •  30) (iv)
  •  31) (iv)
  •  32) (i)
  •  33) (v)
  •  34) (iv)
  •  35) (v)
  •  36) (ii)
  •  37) (v)
  •  38) (iii)
  •  39) (ii)
  •  40) (ii)
  •  41) (ii)
  •  42) (iv)
  •  43) (i)
  •  44) (v)
  •  45) (i)
  •  46) (i)
  •  47) (iii)