Mathematics Class IX

Question 1 of 37

1. Question
1 point(s)
In a parallelogram PQRS, what is the sum of angles P and Q?
- 90°
- 180°
- Obtuse angle
- Acute angle
Correct

Incorrect

Hint

Sum of adjacent angles of a quadrilateral is 180°
Question 2 of 37

2. Question
1 point(s)
In a parallelogram PQRS, if $ \angle P = 123^{\circ} $, then what is the value of $ \angle S $?
- 123°
- 90°
- 57°
- 180°
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}\angle S+132&=180 \\ \angle S&=57 \end{split}\end{equation*}$
Question 3 of 37

3. Question
1 point(s)
If ABCD is a rectangle with $ \angle CDB = 38^{\circ} $, then what is the measure of $ \angle ACD $?
- 52°
- 53°
- 45°
- 38°
Correct

Incorrect

Hint

Angles opposite to equal sides are equal.
Question 4 of 37

4. Question
1 point(s)
If EFGH is a rhombus with $ \angle EFG = 52^{\circ} $, then what is the measure of $ \angle EGH $?
- 64°
- 38°
- 128°
- 34°
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}x+x+52&=180 \\ x&=64 \end{split}\end{equation*}$
Question 5 of 37

5. Question
1 point(s)
If ABCD is a square, then find the value of $\angle ABD $.
- 45°
- 90°
- 60°
- 40°
Correct

Incorrect

Hint

Diagonals of square are angle bisector.
Question 6 of 37

6. Question
1 point(s)
The perimeter of a parallelogram is 19cm. If one side of the parallelogram is 7.5cm, then what is the value of its adjacent side?
- 4cm
- 2cm
- 7.5cm
- 15cm
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}x+x+7.5+7.5&=19 \\ x&=2 \end{split}\end{equation*}$
Question 7 of 37

7. Question
1 point(s)
The angles of a quadrilaterals are in the ratio 6:7:13:14. Find the value of the largest angle.
- 54°
- 63°
- 126°
- 117°
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}6x+7x+13x+14x&=360 \\ 14x&=126 \end{split}\end{equation*}$
Question 8 of 37

8. Question
1 point(s)
The diagonals of a rectangle PQRS meet at O. If $ \angle QOR = 32^{\circ} $, then find the value of $ \angle OPS $?
- 32°
- 74°
- 58°
- 148°
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}x+x+32&=180 \\ x&=74 \end{split}\end{equation*}$
Question 9 of 37

9. Question
1 point(s)
What is the value of angle formed by the intersection of two diagonals of a square?
- 45°
- 60°
- 90°
- 180°
Correct

Incorrect

Hint

Diagonals of a square form 90° angle.
Question 10 of 37

10. Question
1 point(s)
In a quadrilateral PQRS, bisectors of angles P and Q intersect at M such that $ \angle PQM =65°$. Find the value of $ \angle R + \angle S$.
- 180°
- 240°
- 65°
- 130°
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}\dfrac{1}{2}(\angle R + \angle S)&=65 \\ \angle R + \angle S&=130 \end{split}\end{equation*}$
Question 11 of 37

11. Question
1 point(s)
In the following figure, PQRS is a trapezium. Find the value of l.
- 120°
- 110°
- 135°
- 105°
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}4m+2m&=180 \\ m&=30 \\ 2m&=l (angles opposite to equal sides are equal)\\ 60&=l \end{split}\end{equation*}$
Question 12 of 37

12. Question
1 point(s)
In the following figure, ABCD is and isosceles trapezium. Find the value of x and y.
- 110°, 20°
- 20°, 110°
- 45°, 135°
- 25°, 110°
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}3x+10+4x+30&=180 \\ x&=20 \\ 4x+30+y&=180 \\ y&=110 \end{split}\end{equation*}$
Question 13 of 37

13. Question
1 point(s)
One angle of a parallelogram is 32° less than the thrice of the smallest angle. Find the largest angle.
- 159°
- 53°
- 127°
- 180°
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}Let bigger angle y&=3x-32 \\ y+x&=180 \\ 3x-32+x&=180 \\ x&=53 \\ y&=3(53)-32 \\ y&=127 \end{split}\end{equation*}$
Question 14 of 37

14. Question
1 point(s)
In a parallelogram PQRS, if $ \angle PQR=60^{\circ}$ and $\angle SPR = 90^{\circ} $, then find the value of $ \angle SRP$.
- 60°
- 45°
- 90°
- 30°
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}\angle PSR &= \angle PQR \\ 90+60+ \angle SRP &=180 \\ \angle SRP &=30 \end{split}\end{equation*}$
Question 15 of 37

15. Question
1 point(s)
In a rhombus ABCD, if $\angle ADB=42^{/\circ} $, then find the value of $ \angle ACB$.
- 48°
- 45°
- 44°
- 52°
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}\angle ADB &= \angle DBC \\ \angle ACB +42+90&=180 \\ \angle ACB&=48 \end{split}\end{equation*}$
Question 16 of 37

16. Question
1 point(s)
In the following figure, PMNO and PQRS are two parallelogram. If the measure of angle N is 34°, then find the measure of angle R.
- 45°
- 34°
- 30°
- 56°
Correct

Incorrect

Hint

Both parallelograms are similar to each other.
Question 17 of 37

17. Question
1 point(s)
Diagonals of a quadrilateral MNOP bisect each other.If $\angle M=57^[\circ} /latex], then [mathjax][latex]\angle N $ is-
- 105°
- 111°
- 123°
- 120°
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}\angle M + \angle N&=180 \\ \angle N&=123 \end{split}\end{equation*}$
Question 18 of 37

18. Question
1 point(s)
Diagonals of a rhombus are-
- Not equal
- Bisect each other
- Perpendicular to each other
- All of the above
Correct

Incorrect

Hint

Diagonals of a rhombus have all above properties.
Question 19 of 37

19. Question
1 point(s)
If ABCD is a rectangle with $ \angle CDB = 42^{\circ} $, then what is the measure of $ \angle ACD $?
- 42°
- 45°
- 48°
- 55°
Correct

Incorrect

Hint

Angles opposite to equal sides are equal.
Question 20 of 37

20. Question
1 point(s)
If EFGH is a rhombus with $ \angle EFG = 44^{\circ} $, then what is the measure of $ \angle EGH $?
- 66°
- 68°
- 50°
- 45°
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}x+x+44&=180 \\ x&=68 \end{split}\end{equation*}$
Question 21 of 37

21. Question
1 point(s)
The perimeter of a parallelogram is 22cm. If one side of the parallelogram is 8cm, then what is the value of its adjacent side?
- 6cm
- 8cm
- 3cm
- 16cm
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}x+x+8+8&=22 \\ x&=3 \end{split}\end{equation*}$
Question 22 of 37

22. Question
1 point(s)
If opposite angles of a parallelogram are (56+x)° and (4x-34)°, then find the value of other angles.
- 94°, 86°
- 86°, 94°
- 86°, 86°
- 94°, 94°
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}56+x&=4x-34 \\ x&=30 \\ 56+x&=56+30 \\ &=86 \\ Let other angle be y \\ y+86&=180 \\ y&=94\end{split}\end{equation*}$
Question 23 of 37

23. Question
1 point(s)
The diagonals of a parallelogram are equal iff it is a-
- Rectangle
- Rhombus
- Isosceles trapezium
- None of the above
Correct

Incorrect

Hint

The diagonals of a parallelogram are equal iff it is a rectangle.
Question 24 of 37

24. Question
1 point(s)
The diagonals of a parallelogram are perpendicular iff it is a-
- Rectangle
- Rhombus
- Isosceles trapezium
- None of the above
Correct

Incorrect

Hint

The diagonals of a parallelogram are perpendicular iff it is a rhombus.
Question 25 of 37

25. Question
1 point(s)
In parallelogram, the bisectors of an two consecutive angles forms a/an-
- Acute angle
- Obtuse angle
- Right angle
- None of the above
Correct

Incorrect

Hint

In parallelogram, the bisectors of an two consecutive angles forms a right angle.
Question 26 of 37

26. Question
1 point(s)
The diagonals of a rectangle ABCD meet each other at O. If $ \angle ABD = 55^{\circ}$, then $ \angle DOC$=
- 45°
- 55°
- 110°
- 70°
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}55+55+\angle DOC&=180 \\ \angle DOC&=70 \end{split}\end{equation*}$
Question 27 of 37

27. Question
1 point(s)
One angle of a parallelogram is 45° less than the twice of the smallest angle. Find the largest angle.
- 105°
- 110°
- 150°
- 145°
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}Let bigger angle y&=2x-45 \\ y+x&=180 \\ 2x-45+x&=180 \\ x&=75 \\ y&=2(75)-45 \\ y&=105 \end{split}\end{equation*}$
Question 28 of 37

28. Question
1 point(s)
In a parallelogram PQRS, if $ \angle PQR=55^{\circ}$ and $\angle SPR = 82^{\circ} $, then find the value of $ \angle SRP$.
- 45°
- 43°
- 98°
- 40°
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}\angle PSR &= \angle PQR \\ 55+82+ \angle SRP &=180 \\ \angle SRP &=43 \end{split}\end{equation*}$
Question 29 of 37

29. Question
1 point(s)
In a rhombus ABCD, if $\angle ADB=38^{/\circ} $, then find the value of $ \angle ACB$.
- 38°
- 48°
- 52°
- 50°
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}\angle ADB &= \angle DBC \\ \angle ACB +38+90&=180 \\ \angle ACB&=52 \end{split}\end{equation*}$
Question 30 of 37

30. Question
1 point(s)
In a parallelogram PQRS, what is the sum of angles P and R?
- 90°
- 180°
- 135°
- Data inadequate
Correct

Incorrect

Hint

Sum of two opposite angles of a parallelogram cannot be defined using the given data. More data is required to find the exact sum.
Question 31 of 37

31. Question
1 point(s)
If PQRS is an isosceles trapezium, the value of $ \angle R $ is equal to-
- $ \angle S $
- $ \angle P $
- $ \angle Q $
- 90°
Correct

Incorrect

Hint

Angles opposite to equal sides are equal.
Question 32 of 37

32. Question
1 point(s)
How many lines are required to form a quadrilateral?
- 2
- 4
- 3
- 5
Correct

Incorrect

Hint

A quadrilateral has 4 sides.
Question 33 of 37

33. Question
1 point(s)
If AB and CD are two perpendicular diameters of a circle, then ACBD is a-
- Rectangle
- Trapezium
- Square
- Parallelogram
Correct

Incorrect

Hint

If AB and CD are two perpendicular diameters of a circle, then ACBD is a square.
Question 34 of 37

34. Question
1 point(s)
The angles of a quadrilaterals are in the ratio 2:3:5:8. Find the value of the smallest angle.
- 15°
- 60°
- 20°
- 40°
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split}2x+3x+5x+8x&=360 \\ 2x&=40 \end{split}\end{equation*}$
Question 35 of 37

35. Question
1 point(s)
In which case a rectangle can be a square?
- Diagonals bisect each other.
- Diagonals perpendicular to each other.
- Both a and b
- None of the above
Correct

Incorrect

Hint

If diagonals of a rectangle are perpendicular to each othe, then it is a square.
Question 36 of 37

36. Question
1 point(s)
The bisectors of the angles of a parallelogram enclose a-
- Rectangle
- Square
- Rhombus
- Parallelogram
Correct

Incorrect

Hint

The bisectors of the angles of a parallelogram enclose a rectangle.
Question 37 of 37

37. Question
1 point(s)
Which of the following is true regarding the line segment joining the mid-points of two sides of a triangle?
- Parallel to the third side
- Equal to the third side
- Both a and b
- None of the above
Correct

Incorrect

Hint

Line segment joining the mid-points of two sides of a triangle is parallel to the third side.

Mathematics Class IX

Practice Questions-Quadrilaterals-ClassIX

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