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CBSE · Class 9 · Mathematics

Quadrilaterals

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
Three angles of a quadrilateral are 55°, 80°, 104°. The fourth angle is:
  1. 131°
  2. 239°
  3. 59°
  4. 121°
2.
One angle of a parallelogram is 130°. The angle opposite it is:
  1. 130°
  2. 50°
  3. 230°
  4. 40°
3.
The diagonals of a rhombus are 14 cm and 48 cm. Each side of the rhombus is:
  1. 50 cm
  2. 31 cm
  3. 32 cm
  4. 25 cm
4.
A rectangle is 20 cm by 48 cm. Each of its diagonals is:
  1. 28 cm
  2. 68 cm
  3. 53 cm
  4. 52 cm
5.
The angles of a quadrilateral add up to:
  1. 270°
  2. 180°
  3. 360°
  4. 540°
6.
The angles of a quadrilateral are in the ratio 2 : 3 : 3 : 7. The largest angle is:
  1. 168°
  2. 72°
  3. 48°
  4. 192°
7.
In △ABC, D and E are the mid-points of AB and AC. If BC = 38 cm, then DE is:
  1. 20 cm
  2. 38 cm
  3. 76 cm
  4. 19 cm
8.
Assertion (A): In △ABC, D and E are the mid-points of AB and AC. If BC = 12 cm, then DE = 6 cm.
Reason (R): The line segment joining the mid-points of two sides of a triangle equals the third side.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
Two adjacent angles of a parallelogram are (4x + 36)° and (2x + 6)°. Find x and all four angles.
10.
Two opposite angles of a parallelogram are (x + 3)° and (3x − 45)°. Find x and the angles of the parallelogram.
11.
The angles of a quadrilateral are x°, (x + 18)°, 2x° and (2x + 78)°. Find x and the four angles.
12.
The diagonals of a rhombus are 40 cm and 96 cm. Find its side and perimeter.
13.
The diagonals of parallelogram ABCD meet at O. AO = (5x + 29) cm and OC = (2x + 47) cm. Find x and AC.
14.
The sides of a triangle are 21 cm, 26 cm and 8 cm. Find the perimeter of the triangle formed by joining the mid-points of its sides.
15.
ABCD is a rectangle with diagonals AC = (x + 23) cm and BD = (4x − 34) cm. Find x and the length of each diagonal.
16.
The perimeter of a parallelogram is 148 cm and one side is 35 cm. Find the other sides.
Section C — Word problems4 × 4 = 16 marks
17.
A rectangular field is 60 m by 80 m. How much shorter is it to walk along the diagonal than along two sides?
18.
A plot is shaped like a rhombus with diagonals of 120 m and 126 m. Find the length of fencing needed round it.
19.
A triangular park has sides of 90 m, 102 m and 84 m. Paths join the mid-points of the three sides. What is the total length of the paths?
20.
A floor tile is a parallelogram with one angle of 124°. Find its other three angles.
AmbifulWorksheets
Practice that never repeats
CBSE · Class 9 · Mathematics

Answer key

Quadrilaterals · AW-9M-QUD-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) 121°360° − 239° = 121°
2(a) 130°opposite angles are equal
3(d) 25 cmthe diagonals bisect at right angles: √(72 + 242) = 25
4(d) 52 cm√(202 + 482) = 52
5(c) 360°—
6(a) 168°15 parts = 360°, 1 part = 24°
7(d) 19 cmDE = BC ÷ 2 (mid-point theorem)
8(c) A is true, but R is false.A is true: DE = BC ÷ 2 = 6. R is false.
9x = 23; 128°, 52°, 128°, 52°adjacent angles are supplementary: 6x + 42 = 180
10x = 24; 27°, 153°, 27°, 153°opposite angles are equal: −2x = −48
11x = 44; 44°, 62°, 88°, 166°6x + 96 = 360
12side 52 cm, perimeter 208 cmhalf-diagonals 20 and 48 meet at 90°: side = √(202 + 482) = 52
13x = 6; AC = 118 cmthe diagonals bisect each other: AO = OC, so 3x = 18
1427.5 cmeach side of the new triangle is half a side of the old one: 55 ÷ 2
15x = 19; 42 cmthe diagonals of a rectangle are equal: −3x = −57
1635 cm, 39 cm, 35 cm, 39 cmopposite sides are equal: 2 × (35 + y) = 148, y = 39
1740 mdiagonal = √(602 + 802) = 100 m; 140 − 100 = 40
18348 mside = √(602 + 632) = 87 m; 4 × 87
19138 meach path is half the side it is parallel to (mid-point theorem)
2056°, 124° and 56°adjacent angles add to 180°; opposite angles are equal