EduSahara™ Assignment
Name : Quadrilateral Angle Properties
Chapter : Understanding Quadrilaterals
Grade : CBSE Grade VIII
License : Non Commercial Use
Question 1
1.
    • The measures of three angles of a quadrilateral are
    • 59.3°
    • ,
    • 125.88°
    • and
    • 57.2°
    • . Find the fourth angle
  • (i)
    122.62°
  • (ii)
    117.62°
  • (iii)
    147.62°
  • (iv)
    127.62°
  • (v)
    132.62°
Question 2
2.
Sum of the interior angles in a quadrilateral is
  • (i)
    370°
  • (ii)
    365°
  • (iii)
    390°
  • (iv)
    375°
  • (v)
    360°
Question 3
3.
Find the missing angle in the given quadrilateral
  • (i)
    121.81°
  • (ii)
    116.81°
  • (iii)
    106.81°
  • (iv)
    111.81°
  • (v)
    136.81°
Question 4
4.
Find the missing angle in the given trapezium
  • (i)
    107.06°
  • (ii)
    137.06°
  • (iii)
    112.06°
  • (iv)
    122.06°
  • (v)
    117.06°
Question 5
5.
Find the missing angle in the given parallelogram
  • (i)
    80.1°
  • (ii)
    95.1°
  • (iii)
    85.1°
  • (iv)
    110.1°
  • (v)
    90.1°
Question 6
6.
Find the missing angle in the given rhombus
  • (i)
    138.12°
  • (ii)
    118.12°
  • (iii)
    108.12°
  • (iv)
    113.12°
  • (v)
    123.12°
Question 7
7.
In parallelogram ABCD, if ∠D = 110.02°, then find the value of ∠C
  • (i)
    69.98°
  • (ii)
    71.98°
  • (iii)
    67.98°
  • (iv)
    70.98°
  • (v)
    68.98°
Question 8
8.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
  • (i)
    90°
  • (ii)
    89°
  • (iii)
    91°
  • (iv)
    92°
  • (v)
    88°
Question 9
9.
If ABCD is an isosceles trapezium, ∠D =
  • (i)
    90°
  • (ii)
    ∠A
  • (iii)
    ∠C
  • (iv)
    ∠B
Question 10
10.
BCDE is a rhombus in which ∠B = 120° .
 

CE
 
 
is the diagonal. Then △BCD is
  • (i)
    an isosceles triangle
  • (ii)
    a scalene triangle
  • (iii)
    an equilateral triangle
  • (iv)
    None of these
  • (v)
    an obtuse angled triangle
Question 11
11.
HIJK is a rhombus in which ∠H = 115° .
 

IK
 
 
is the diagonal. Then △HIJ is
  • (i)
    None of these
  • (ii)
    an isosceles triangle
  • (iii)
    an obtuse angled triangle
  • (iv)
    a scalene triangle
  • (v)
    an equilateral triangle
Question 12
12.
The angles of a quadrilateral EFGH are in the ratio 4 : 16 : 8 : 32. Find the measure of each angle of the quadrilateral.
  • (i)
    E
    =
    23°
    ,
    F
    =
    94°
    ,
    G
    =
    49°
    ,
    H
    =
    194°
  • (ii)
    E
    =
    22°
    ,
    F
    =
    98°
    ,
    G
    =
    47°
    ,
    H
    =
    193°
  • (iii)
    E
    =
    26°
    ,
    F
    =
    95°
    ,
    G
    =
    46°
    ,
    H
    =
    193°
  • (iv)
    E
    =
    25°
    ,
    F
    =
    95°
    ,
    G
    =
    50°
    ,
    H
    =
    190°
  • (v)
    E
    =
    24°
    ,
    F
    =
    96°
    ,
    G
    =
    48°
    ,
    H
    =
    192°
Question 13
13.
Two adjacent angles of a parallelogram KLMN are in the ratio 9 : 21. Find the measure of each of its angles.
  • (i)
    K
    =
    52°
    ,
    L
    =
    128°
    ,
    M
    =
    53°
    ,
    N
    =
    127°
  • (ii)
    K
    =
    53°
    ,
    L
    =
    124°
    ,
    M
    =
    55°
    ,
    N
    =
    128°
  • (iii)
    K
    =
    56°
    ,
    L
    =
    125°
    ,
    M
    =
    52°
    ,
    N
    =
    127°
  • (iv)
    K
    =
    55°
    ,
    L
    =
    125°
    ,
    M
    =
    56°
    ,
    N
    =
    124°
  • (v)
    K
    =
    54°
    ,
    L
    =
    126°
    ,
    M
    =
    54°
    ,
    N
    =
    126°
Question 14
14.
    • In the adjoining figure,
    • MNOP
    • is a parallelogram in which
    • ∠PMO = 20.92°
    • ,
    • ∠OMN = 23.63°
    • ,
    • ∠PQO = 80.62°
    • . Calculate
    • ∠MNP
  • (i)
    74.75°
  • (ii)
    75.75°
  • (iii)
    73.75°
  • (iv)
    77.75°
  • (v)
    76.75°
Question 15
15.
    • In the adjoining figure,
    • KLMN
    • is a parallelogram in which
    • ∠NKM = 17.83°
    • ,
    • ∠MKL = 33.06°
    • ,
    • ∠NOM = 51.1°
    • . Calculate
    • ∠MNL
  • (i)
    93.84°
  • (ii)
    94.84°
  • (iii)
    96.84°
  • (iv)
    95.84°
  • (v)
    97.84°
Question 16
16.
    • In the adjoining figure,
    • GHIJ
    • is a parallelogram in which
    • ∠JGI = 31.74°
    • ,
    • ∠IGH = 28.05°
    • ,
    • ∠JKI = 97.58°
    • . Calculate
    • ∠HIG
  • (i)
    33.74°
  • (ii)
    29.74°
  • (iii)
    30.74°
  • (iv)
    31.74°
  • (v)
    32.74°
Question 17
17.
    • In the adjoining figure,
    • JKLM
    • is a parallelogram in which
    • ∠MJL = 24.56°
    • ,
    • ∠LJK = 34.75°
    • ,
    • ∠MNL = 68.59°
    • . Calculate
    • ∠MKL
  • (i)
    46.03°
  • (ii)
    43.03°
  • (iii)
    45.03°
  • (iv)
    44.03°
  • (v)
    42.03°
Question 18
18.
    • In the adjoining figure,
    • ABCD
    • is a rectangle.
    • If
    • ∠CAB = 46.85°
    • , find
    • ∠ABD
  • (i)
    48.85°
  • (ii)
    44.85°
  • (iii)
    47.85°
  • (iv)
    45.85°
  • (v)
    46.85°
Question 19
19.
Three angles of quadrilateral measure 107.66°, 82.8° and 52.26° respectively. Find the measure of the fourth angle
  • (i)
    115.28°
  • (ii)
    118.28°
  • (iii)
    119.28°
  • (iv)
    116.28°
  • (v)
    117.28°
Question 20
20.
Three angles of a quadrilateral are equal and the fourth angle measure 111.8°. What is the measure of each of the equal angles?
  • (i)
    81.73°
  • (ii)
    82.73°
  • (iii)
    83.73°
  • (iv)
    80.73°
  • (v)
    84.73°
Question 21
21.
Two angles of a quadrilateral are of measure 72.44° and 109.62° respectively and the other two angles are equal. Find the measure of each of the equal angles.
  • (i)
    88.97°
  • (ii)
    86.97°
  • (iii)
    90.97°
  • (iv)
    87.97°
  • (v)
    89.97°
Question 22
22.
A quadrilateral has three acute angles, each measuring 78°. What is the measure of its fourth angle?
  • (i)
    124.00°
  • (ii)
    126.00°
  • (iii)
    125.00°
  • (iv)
    127.00°
  • (v)
    128.00°
Question 23
23.
    • One angle of a parallelogram measures
    • F
    • =
    • 68.68°
    • .
    • Find the measure of each of its remaining angles.
  • (i)
    G
    =
    111.32°
    ,
    H
    =
    68.68°
    ,
    I
    =
    111.32°
  • (ii)
    G
    =
    109.32°
    ,
    H
    =
    66.68°
    ,
    I
    =
    109.32°
  • (iii)
    G
    =
    112.32°
    ,
    H
    =
    69.68°
    ,
    I
    =
    112.32°
  • (iv)
    G
    =
    113.32°
    ,
    H
    =
    70.68°
    ,
    I
    =
    113.32°
  • (v)
    G
    =
    110.32°
    ,
    H
    =
    67.68°
    ,
    I
    =
    110.32°
Question 24
24.
    • Two adjacent angles of a parallelogram are in the ratio
    • 7 : 23
    • .
    • Find the measure of each of its angles.
  • (i)
    A
    =
    42°
    ,
    B
    =
    138°
    ,
    C
    =
    42°
    ,
    D
    =
    138°
  • (ii)
    A
    =
    44°
    ,
    B
    =
    137°
    ,
    C
    =
    40°
    ,
    D
    =
    139°
  • (iii)
    A
    =
    41°
    ,
    B
    =
    136°
    ,
    C
    =
    43°
    ,
    D
    =
    140°
  • (iv)
    A
    =
    43°
    ,
    B
    =
    137°
    ,
    C
    =
    44°
    ,
    D
    =
    136°
  • (v)
    A
    =
    40°
    ,
    B
    =
    140°
    ,
    C
    =
    41°
    ,
    D
    =
    139°
Question 25
25.
    • In the figure given below,
    • PQRS
    • is a rectangle.
    • Find the values of x and y
  • (i)
    x
    =
    40.18°
    ,
    y
    =
    81.36°
  • (ii)
    x
    =
    43.18°
    ,
    y
    =
    84.36°
  • (iii)
    x
    =
    42.18°
    ,
    y
    =
    83.36°
  • (iv)
    x
    =
    41.18°
    ,
    y
    =
    82.36°
  • (v)
    x
    =
    39.18°
    ,
    y
    =
    80.36°
Question 26
26.
    • In the figure given below,
    • ABCD
    • is a rectangle.
    • Find the values of x and y
  • (i)
    x
    =
    46.12°
    ,
    y
    =
    41.88°
  • (ii)
    x
    =
    47.12°
    ,
    y
    =
    42.88°
  • (iii)
    x
    =
    49.12°
    ,
    y
    =
    44.88°
  • (iv)
    x
    =
    45.12°
    ,
    y
    =
    40.88°
  • (v)
    x
    =
    48.12°
    ,
    y
    =
    43.88°
Question 27
27.
    • In the figure given below,
    • MNOP
    • is a rhombus.
    • Find the values of x and y
  • (i)
    x
    =
    21.66°
    ,
    y
    =
    21.66°
  • (ii)
    x
    =
    22.66°
    ,
    y
    =
    22.66°
  • (iii)
    x
    =
    23.66°
    ,
    y
    =
    23.66°
  • (iv)
    x
    =
    20.66°
    ,
    y
    =
    20.66°
  • (v)
    x
    =
    24.66°
    ,
    y
    =
    24.66°
Question 28
28.
    • In the figure given below,
    • CDEF
    • is a rhombus.
    • Find the values of x and y
  • (i)
    x
    =
    36.33°
    ,
    y
    =
    36.33°
  • (ii)
    x
    =
    37.33°
    ,
    y
    =
    37.33°
  • (iii)
    x
    =
    34.33°
    ,
    y
    =
    34.33°
  • (iv)
    x
    =
    35.33°
    ,
    y
    =
    35.33°
  • (v)
    x
    =
    33.33°
    ,
    y
    =
    33.33°
Question 29
29.
    • In the figure given below,
    • ABCD
    • is a rhombus.
    • Find the values of x and y
  • (i)
    x
    =
    36.93°
    ,
    y
    =
    57.07°
  • (ii)
    x
    =
    33.93°
    ,
    y
    =
    54.07°
  • (iii)
    x
    =
    34.93°
    ,
    y
    =
    55.07°
  • (iv)
    x
    =
    32.93°
    ,
    y
    =
    53.07°
  • (v)
    x
    =
    35.93°
    ,
    y
    =
    56.07°
Question 30
30.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
  • (i)
    O
    =
    59°
    ,
    P
    =
    118°
    ,
    Q
    =
    61°
    ,
    R
    =
    122°
  • (ii)
    O
    =
    60°
    ,
    P
    =
    120°
    ,
    Q
    =
    60°
    ,
    R
    =
    120°
  • (iii)
    O
    =
    58°
    ,
    P
    =
    122°
    ,
    Q
    =
    59°
    ,
    R
    =
    121°
  • (iv)
    O
    =
    61°
    ,
    P
    =
    119°
    ,
    Q
    =
    62°
    ,
    R
    =
    118°
  • (v)
    O
    =
    62°
    ,
    P
    =
    119°
    ,
    Q
    =
    58°
    ,
    R
    =
    121°
Question 31
31.
    • In the adjoining figure,
    • BCDE
    • is a trapezium in which
    •  

      BC
       
       
      ∥
       

      DE
       
       
    • .
    • If
    •  
    • x = 51.26°
    • and
    •  
    • y = 82.71°
    • ,
    • find the measures of
    • ∠D
    • and
    • ∠E
    • .
  • (i)
    D
    =
    99.29°
    ,
    E
    =
    130.74°
  • (ii)
    D
    =
    98.29°
    ,
    E
    =
    129.74°
  • (iii)
    D
    =
    96.29°
    ,
    E
    =
    127.74°
  • (iv)
    D
    =
    95.29°
    ,
    E
    =
    126.74°
  • (v)
    D
    =
    97.29°
    ,
    E
    =
    128.74°
Question 32
32.
    • 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 = 33.37° and ∠ABO = 58.71°, find the measure of each of the angles marked a,b,c,d and e.
  • (i)
    a = 56.63° , b = 32.29° , c = 57.71° , d = 58.63° , e = 33.37°
  • (ii)
    a = 56.63° , b = 32.29° , c = 57.71° , d = 56.63° , e = 33.37°
  • (iii)
    a = 56.63° , b = 32.29° , c = 58.71° , d = 56.63° , e = 33.37°
  • (iv)
    a = 56.63° , b = 32.29° , c = 57.71° , d = 58.63° , e = 31.37°
  • (v)
    a = 56.63° , b = 31.29° , c = 58.71° , d = 56.63° , e = 33.37°
Question 33
33.
In the adjoining figure, side KH of parallelogram HIJK has been produced to L. If ∠IHL = 120.14° , find the measure of each angle of the parallelogram.
  • (i)
    H
    =
    57.86°
    ,
    I
    =
    122.14°
    ,
    J
    =
    58.86°
    ,
    K
    =
    121.14°
  • (ii)
    H
    =
    59.86°
    ,
    I
    =
    120.14°
    ,
    J
    =
    59.86°
    ,
    K
    =
    120.14°
  • (iii)
    H
    =
    60.86°
    ,
    I
    =
    119.14°
    ,
    J
    =
    61.86°
    ,
    K
    =
    118.14°
  • (iv)
    H
    =
    61.86°
    ,
    I
    =
    119.14°
    ,
    J
    =
    57.86°
    ,
    K
    =
    121.14°
  • (v)
    H
    =
    58.86°
    ,
    I
    =
    118.14°
    ,
    J
    =
    60.86°
    ,
    K
    =
    122.14°
Question 34
34.
    • In the adjoining figure,
    • NOPQ
    • is a parallelogram and
    • RS
    • is such that
    •  

      RS
       
       
      ∥
       

      NP
       
       
    • If
    • ∠NQR = 35.63°
    • and
    • ∠PQS = 27.4°
    • ,
    • find the measure of
    • ∠PQN
    • .
  • (i)
    114.97°
  • (ii)
    116.97°
  • (iii)
    117.97°
  • (iv)
    115.97°
  • (v)
    118.97°
Question 35
35.
In the adjoining figure, GHIJ is a square. A line segment JL cuts the side HI at L and the diagonal GI at K such that ∠JKI = 105.64° and ∠KLI = x°. Find the value of x .
  • (i)
    60.64°
  • (ii)
    61.64°
  • (iii)
    62.64°
  • (iv)
    59.64°
  • (v)
    58.64°
Question 36
36.
In the adjoining figure, ABCD is a rhombus and △EDC is an equilateral triangle. E and B are on opposite sides of  CD. If ∠DAB = 65.01°, find the values of  x  and  y .
  • (i)
    x
    =
    30°
    ,
    y
    =
    27.49°
  • (ii)
    x
    =
    29°
    ,
    y
    =
    26.49°
  • (iii)
    x
    =
    28°
    ,
    y
    =
    25.49°
  • (iv)
    x
    =
    31°
    ,
    y
    =
    28.49°
  • (v)
    x
    =
    32°
    ,
    y
    =
    29.49°
Question 37
37.
In the adjoining figure, equilateral  △POQ surmounts square  MNOP. If  OQN = x°, find the value of x.
  • (i)
    14°
  • (ii)
    17°
  • (iii)
    16°
  • (iv)
    13°
  • (v)
    15°
Question 38
38.
    • In the adjoining figure,
    • ABCD
    • is a rhombus whose diagonals intersect at
    • O
    • .
    • If
    • ∠OAB
    • :
    • ∠ABO
    • =
    • 2 : 13
    • ,
    • find the angles of
    • △OAB
    • .
  • (i)
    O
    =
    88°
    ,
    A
    =
    12°
    ,
    B
    =
    80°
  • (ii)
    O
    =
    88°
    ,
    A
    =
    14°
    ,
    B
    =
    78°
  • (iii)
    O
    =
    90°
    ,
    A
    =
    10°
    ,
    B
    =
    80°
  • (iv)
    O
    =
    92°
    ,
    A
    =
    12°
    ,
    B
    =
    76°
  • (v)
    O
    =
    90°
    ,
    A
    =
    12°
    ,
    B
    =
    78°
Question 39
39.
    • In the given figure,
    • OPQR
    • is a rectangle whose diagonals intersect at
    • S
    • .
    • Diagonal
    • OQ
    • is produced to
    • T
    • and
    • ∠RQT =
    • 143.13°
    • . Find the angles of
    • △SOP
    • .
  • (i)
    S
    =
    104.26°
    ,
    O
    =
    38.87°
    ,
    P
    =
    36.87°
  • (ii)
    S
    =
    106.26°
    ,
    O
    =
    36.87°
    ,
    P
    =
    36.87°
  • (iii)
    S
    =
    104.26°
    ,
    O
    =
    36.87°
    ,
    P
    =
    38.87°
  • (iv)
    S
    =
    106.26°
    ,
    O
    =
    34.87°
    ,
    P
    =
    38.87°
  • (v)
    S
    =
    108.26°
    ,
    O
    =
    36.87°
    ,
    P
    =
    34.87°
Question 40
40.
    • In the given figure,
    • OPQR
    • is a kite whose diagonals intersect at
    • S
    • .
    • If
    • ∠ROP = 53.42°
    • and
    • ∠OPQ = 129.68°
    • , calculate
    • ∠SRO
    • and
    • ∠SQR
    • .
  • (i)
    x
    =
    62.29°
    ,
    y
    =
    22.61°
  • (ii)
    x
    =
    63.29°
    ,
    y
    =
    23.61°
  • (iii)
    x
    =
    61.29°
    ,
    y
    =
    21.61°
  • (iv)
    x
    =
    65.29°
    ,
    y
    =
    25.61°
  • (v)
    x
    =
    64.29°
    ,
    y
    =
    24.61°
Question 41
41.
    • △ECD
    • is an equilateral triangle in a square
    • ABCD
    • .
    • If
    • BD
    • and
    • EC
    • intersect at
    • F
    • ,
    • then find the value of x.
  • (i)
    77°
  • (ii)
    76°
  • (iii)
    73°
  • (iv)
    75°
  • (v)
    74°
Question 42
42.
    • In the adjoining figure,
    • F
    • is a point in the interior of
    • ∠HDI
    • .
    • If
    •  
    • FE
    • ⟂
    • DH
    • and
    • FG
    • ⟂
    • DI
    • and
    • ∠HDI = 59°
    • ,
    • find the measure of x .
  • (i)
    120°
  • (ii)
    119°
  • (iii)
    123°
  • (iv)
    121°
  • (v)
    122°
    Assignment Key
  •  1) (ii)
  •  2) (v)
  •  3) (iii)
  •  4) (i)
  •  5) (i)
  •  6) (iii)
  •  7) (i)
  •  8) (i)
  •  9) (iii)
  •  10) (iii)
  •  11) (ii)
  •  12) (v)
  •  13) (v)
  •  14) (ii)
  •  15) (iv)
  •  16) (iv)
  •  17) (iv)
  •  18) (v)
  •  19) (v)
  •  20) (ii)
  •  21) (i)
  •  22) (ii)
  •  23) (i)
  •  24) (i)
  •  25) (iv)
  •  26) (ii)
  •  27) (ii)
  •  28) (iv)
  •  29) (iii)
  •  30) (ii)
  •  31) (v)
  •  32) (v)
  •  33) (ii)
  •  34) (ii)
  •  35) (i)
  •  36) (i)
  •  37) (v)
  •  38) (v)
  •  39) (ii)
  •  40) (ii)
  •  41) (iv)
  •  42) (iv)