Quadrilaterals Test

Result

Quadrilaterals Test - 7

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Question 1
1 / -0

In the given figure A + B is 170°, what is the measure of C + D?

A
170°

B
180°

C
190°

D
200°

Solution

A + B + C + D = 360°
170° + C + D = 360°
C + D = 190°
Question 2
1 / -0

The diagonals of a parallelogram ABCD intersect at O. If BAC = 40° and BDC = 60°, then AOB is

A
10°

B
80°

C
50°

D
90°

Solution

D = B = 60°
B + A + O = 180°
40° + 60° + O = 180°
O = 80°
AOB = 80°
Question 3
1 / -0

The diagonals of a rectangle ABCD cut at K. If AKB = 110°, then ACB and ACD are respectively equal to

A
55°, 45°

B
45°, 55°

C
55°, 35°

D
35°, 55°

Solution

z = 110° (Vertically opposite angles)
y = 180° - z - CDB
CDB = y (Angles opposite to equal sides)
2y = 70°
y = 35°
x = 90° - 35° = 55°
Question 4
1 / -0

In the given figure, AO and DO are the bisectors of A and D respectively of the quadrilateral ABCD. AOD is equal to

A
67.5°

B
77°

C
90°

D
99.75°

Solution

If ABCD is a parallelogram, then
A = 180°- B = 180° - 70° = 110°
or, A = 55°
OAD = 55°
D = 180°- C= 180° - 110° = 70°
or, D = 35°
ODA = 35°
In triangle ADO, AOD = 180°- OAD - ODA = 180° - 35° - 55° = 90°
Question 5
1 / -0

A diagonal of a rectangle is inclined to one side of the rectangle at 30°. The acute angle between the diagonals is

A
25°

B
40°

C
60°

D
55°

Solution
Question 6
1 / -0

The diagonals of a rectangle ABCD cut at N. If ABD = 74⁰, then DNC is equal to

A
32⁰

B
64⁰

C
148⁰

D
74⁰

Solution

y = x
And y = 180° - 74° - 74°
= 180° - 148°
= 32°
x = 32°
Question 7
1 / -0

In the given figure, ABCD is a trapezium in which AB = 7 cm, AD = BC = 13 cm, DC = x cm and the distance between AB and DC is 5 cm. The value of x is

A
31 cm

B
25 cm

C
19 cm

D
cannot be determined

Solution

L = √(13² - 5²) = 12
M = √((13² - 5²) = 12
DC = 12 + 7 + 12 = 31 cm
Question 8
1 / -0

ABCD is a rhombus. If ACB = 50°, then ADB is

A
50°

B
45°

C
40°

D
60°

Solution

y = 180° - 50° - 90°
= 40°
Now, x = y (Alternate angles)
x = 40°
Question 9
1 / -0

ABCD is a square. A straight line CPQ cuts BD at P and BA is produced at Q. If CPD = 80⁰, then CQA is equal to

A
35⁰

B
55⁰

C
45⁰

D
10⁰

Solution

y = 180° - 80° - 45°
= 55°
x = y = 55° (Alternate angles)
Question 10
1 / -0

What is the sum of the angles of a quadrilateral?

A
180°

B
360°

C
270°

D
Depends on the quadrilateral

Solution

Sum of angles of an n-sided polygon = (n – 2)180°
For a quadrilateral, n = 4.
Sum of angles of a quadrilateral = (4 – 2)180° = 360°
Question 11
1 / -0

The quadrilateral formed by joining the midpoints of the sides of a quadrilateral PQRS, taken in order, is a rectangle if

A
PQRS is a rectangle

B
PQRS is a parallelogram

C
diagonals of PQRS are perpendicular

D
diagonals of PQRS are equal

Solution

The quadrilateral formed by joining the midpoints of the sides of quadrilateral PQRS, taken in order, is a rectangle if the diagonals of PQRS are perpendicular.
Question 12
1 / -0

PQRS is a parallelogram, PT is perpendicular to SR and RV is perpendicular to PS. If PQ = 16 cm, PT = 8 cm and VR = 10 cm, then find PS.

A
10 cm

B
10.8 cm

C
12 cm

D
12.8 cm

Solution

Area of parallelogram PQRS = SR x PT = 16 x 8 cm². (Because PQ = SR, PQRS is a parallelogram)
= 128 cm² …(1)
Also, area of parallelogram PQRS = VR x PS = 16 x 8 cm² = 128 cm² … (2)
From (1) and (2), we get
10 x PS = 128
So, PS = 128/10 = 12.8 cm
Question 13
1 / -0

If ABCD is an isosceles trapezium, C is equal to

A
B

B
A

C
D

D
90°

Solution

For isosceles trapezium, C = B.
So, option (3) is correct.
Question 14
1 / -0

The quadrilateral formed by joining the mid points of the sides of a quadrilateral PQRS, taken in order is a rhombus if

A
PQRS is a rhombus

B
PQRS is a parallelogram

C
diagonals of PQRS are perpendicular

D
diagonals of PQRS are equal

Solution

The quadrilateral formed by joining the midpoints of the sides of quadrilateral PQRS, taken in order, is a rhombus if the diagonals of PQRS are equal in length.
Question 15
1 / -0

In the given figure, ABCD is a parallelogram, where BL and DM are perpendicular to AC. Which of the following relations holds true?

A
DM = BL

B
DM + BL = AC

C
DM = AC

D
2DM = AC

Solution

Perpendiculars drawn on the same diagonals of a IIgm from opposite vertices are always equal in length.
Question 16
1 / -0

The number of measurements required to construct a quadrilateral is

A
5

B
4

C
3

D
2

Solution

We must have a minimum of 4 measurements to construct a quadrilateral.
Question 17
1 / -0

If angles P, Q, R and S of a quadrilateral PQRS are in the ratio of 3 : 7 : 6 : 4, then PQRS is a

A
rhombus

B
parallelogram

C
trapezium

D
kite

Solution

Sum of angles of a quadrilateral = 360°
3x + 7x + 6x + 4x = 360°
20x = 360°
x = 18°
The angles measure 54°, 126°, 108° and 72°.
It is a trapezium as ^_P+ ^_Q = 180°
And, ^_R + ^_S = 180°

Co-interior angles are supplementary for a pair of parallel lines.
Question 18
1 / -0

Sides QP and SR of a quadrilateral PQRS are produced as shown in figure. In this case, a + b is equal to

A
x - y

B
x + y

C
x + 2y

D
x - 2y

Solution

a + b = x + y (Sum of alternate angles)
Question 19
1 / -0

To construct a parallelogram, the minimum number of measurements required is

A
2

B
3

C
4

D
1

Solution

We must have a minimum of 3 measurements.
Question 20
1 / -0

If PQ and RS are two perpendicular diameters of a circle, then PRQS is a

A
rectangle

B
trapezium

C
square

D
rhombus but not square

Solution

Square