Grade 9 : Mathematics - 10. Quadrilaterals (Set 2)

Question 1

A surveyor is measuring four angles of a quadrilateral boundary line. Three of the interior angles measured are $75^\circ$, $90^\circ$, and $105^\circ$.

What is the measure of the fourth interior angle?

Accepted Answer

B) $90^\circ$

Answer

A) $80^\circ$

Answer

C) $100^\circ$

Answer

D) $110^\circ$

Question 2

In a parallelogram ABCD, if $\angle A = 70^\circ$, what is the measure of its adjacent angle $\angle B$?

Accepted Answer

A) $110^\circ$

Answer

B) $70^\circ$

Answer

C) $120^\circ$

Answer

D) $90^\circ$

Question 3

A garden layout is designed in the shape of a rhombus. The lengths of its two intersecting diagonals are 12 m and 16 m.

What is the length of each side of the garden?

Accepted Answer

A) 10 m

Answer

B) 14 m

Answer

C) 20 m

Answer

D) 28 m

Question 4

In a kite-shaped frame PQRS, $PQ = PS = 8cm$ and $QR = SR = 15cm$. What is the total perimeter of the frame?

Accepted Answer

B) 46 cm

Answer

A) 30 cm

Answer

C) 23 cm

Answer

D) 52 cm

Question 5

In quadrilateral ABCD, diagonals AC and BD bisect each other at point $O$. If $AO = 5cm$ and $BO = 7cm$, find the total lengths of diagonals AC and BD.

Accepted Answer

A) $AC = 10cm, BD = 14cm$

Answer

B) $AC = 5cm, BD = 7cm$

Answer

C) $AC = 12cm, BD = 14cm$

Answer

D) $AC = 10cm, BD = 12cm$

Question 6

In a trapezium ABCD with $AB \parallel CD$, if $\angle C = 110^\circ$, what is the measure of $\angle B$?

Accepted Answer

B) $70^\circ$

Answer

A) $60^\circ$

Answer

C) $80^\circ$

Answer

D) $110^\circ$

Question 7

The interior angles of a quadrilateral are in the ratio $2 : 3 : 4 : 6$. What is the measure of the smallest angle?

Accepted Answer

B) $48^\circ$

Answer

A) $36^\circ$

Answer

C) $72^\circ$

Answer

D) $96^\circ$

Question 8

In rectangle ABCD, diagonal $AC = (3x + 4)cm$ and diagonal $BD = (2x + 9)cm$. What is the value of $x$?

Accepted Answer

C) 5

Answer

A) 3

Answer

B) 4

Answer

D) 6

Question 9

In $ riangle ABC$, points $D$ and $E$ are the mid-points of sides AB and AC respectively.

If segment $DE = 9.5cm$, what is the length of side BC?

Accepted Answer

A) 19 cm

Answer

B) 18 cm

Answer

C) 14.25 cm

Answer

D) 9.5 cm

Question 10

In square DEFG, each side length is 12 cm. What is the exact length of its diagonal DF?

Accepted Answer

C) $12\sqrt{2}cm$

Answer

A) 12 cm

Answer

B) 24 cm

Answer

D) 144 cm

Question 11

A rectangular courtyard ABCD has length $AB = 24m$ and width $BC = 10m$.

Calculate the length of the straight pathway along diagonal AC.

Accepted Answer

C) 26 m

Answer

A) 34 m

Answer

B) 28 m

Answer

D) 25 m

Question 12

In parallelogram XYZW, $\angle X = (2x + 10)^\circ$ and opposite angle $\angle Z = (3x - 20)^\circ$. What is the value of $x$?

Accepted Answer

D) 30

Answer

A) 15

Answer

B) 20

Answer

C) 25

Question 13

If P, Q, R, S are the mid-points of sides AB, BC, CD, DA of any arbitrary quadrilateral ABCD, what geometric figure is always formed by PQRS?

Accepted Answer

C) Parallelogram

Answer

A) Rectangle

Answer

B) Rhombus

Answer

D) Square

Question 14

In rhombus ABCD, diagonal BD makes an angle $\angle ABD = 35^\circ$ with side AB. What is the measure of angle $\angle ABC$?

Accepted Answer

B) $70^\circ$

Answer

A) $35^\circ$

Answer

C) $110^\circ$

Answer

D) $140^\circ$

Question 15

Two adjacent interior angles of a parallelogram are in the ratio $4 : 5$. What is the measure of the larger angle?

Accepted Answer

B) $100^\circ$

Answer

A) $80^\circ$

Answer

C) $120^\circ$

Answer

D) $140^\circ$

Question 16

In an isosceles trapezium ABCD where $AB \parallel CD$ and non-parallel sides $AD = BC$, if $\angle A = 65^\circ$, what is $\angle B$?

Accepted Answer

A) $65^\circ$

Answer

B) $115^\circ$

Answer

C) $125^\circ$

Answer

D) $75^\circ$

Question 17

A square park has diagonal length 18 m. What is the total area of the park?

Accepted Answer

B) $162m^2$

Answer

A) $324m^2$

Answer

C) $81m^2$

Answer

D) $144m^2$

Question 18

In quadrilateral ABCD, the sum of opposite angles $\angle A + \angle C = 200^\circ$. What is the sum of the remaining two angles $\angle B + \angle D$?

Accepted Answer

A) $160^\circ$

Answer

B) $180^\circ$

Answer

C) $200^\circ$

Answer

D) $140^\circ$

Question 19

In $ riangle ABC$, $D$ and $E$ are midpoints of sides AB and AC. A smaller triangle $ riangle ADE$ is formed with perimeter 18 cm.

What is the perimeter of the larger triangle $ riangle ABC$?

Accepted Answer

C) 36 cm

Answer

A) 18 cm

Answer

B) 27 cm

Answer

D) 54 cm

Question 20

A quadrilateral has four equal side lengths, equal diagonal lengths, and diagonals that intersect at right angles ($90^\circ$). Which specific quadrilateral is this?

Accepted Answer

C) Square

Answer

A) Rectangle

Answer

B) Rhombus

Answer

D) Trapezium

Grade 9 : Mathematics - 10. Quadrilaterals (Set 2)