MCQ 511 Mark
For which of the following figures, diagonals are equal?
AnswerBy the property of a rectangle, we know that its diagonals are equal.
View full question & answer→MCQ 521 Mark
$ABCD$ is a rhombus. If $\angle\text{ACB}=40^\circ$ then, $\angle\text{ADB}$ is:
- A
$45^\circ$
- B
$60^\circ$
- ✓
$50^\circ$
- D
$40^\circ$
AnswerCorrect option: C. $50^\circ$
$50^\circ$
View full question & answer→MCQ 531 Mark
Which of the following is a property of a parallelogram?
- ✓
Opposite sides are parallel.
- B
The diagonals bisect each other at right angles.
- C
The diagonals are perpendicular to each other.
- D
AnswerCorrect option: A. Opposite sides are parallel.
We, know that, in a parallelogram, opposite sides are parallel.
View full question & answer→MCQ 541 Mark
A quadrilateral whose all sides are equal, opposite angles are equal and the diagonals bisect each other at right angles is a $..........$
AnswerWe know that, in rhombus, all sides are equal, opposite angles are equal and diagonals bisect each other at right angles.
View full question & answer→MCQ 551 Mark
The perimeter of a parallelogram whose parallel sides have lengths equal to $12\ cm$ and $7\ cm$ is:
- A
$19\ cm$
- ✓
$38\ cm$
- C
$21\ cm$
- D
$42\ cm$
AnswerCorrect option: B. $38\ cm$
Perimeter of parallelogram $= 2$ (Sum of Parallel sides)
$P = 2 (12 + 7)$
$P = 2 (19)$
$P = 38\ cm$
View full question & answer→MCQ 561 Mark
If the sides of a triangle are produced in order, What is the sum of the exterior angles so formed?
- A
$540^\circ$
- B
$180^\circ$
- C
$720^\circ$
- ✓
$360^\circ$
AnswerCorrect option: D. $360^\circ$
$360^\circ$
View full question & answer→MCQ 571 Mark
Which of the following quadrilaterals has two pairs of adjacent sides equal and diagonals intersecting at right angles?
Answer
$\Rightarrow $ In given quadrilateral $ABCD$ is a kite
$\Rightarrow $ We know the properties of kite.
$\Rightarrow $ Kite has two pairs of adjacent sides equal.
$\Rightarrow AB = AC$ and $BD = CD$
$\Rightarrow $ In kite it's opposite sides are unequal.
$\Rightarrow $ So, If a quadrilateral has exactly two pairs of equal adjacent sides and the unequal opposite sides, then it is called kite. View full question & answer→MCQ 581 Mark
The measure of each exterior angle of a regular polygon of $15$ sides is:
- A
$30^\circ$
- B
$45^\circ$
- C
$60^\circ$
- ✓
$24^\circ$
AnswerCorrect option: D. $24^\circ$
$24^\circ $
View full question & answer→MCQ 591 Mark
A quadrilateral whose all sides, diagonals and angles are equal is a.
AnswerThese are the properties of a square, i.e. in a square, all sides, diagonals and angles are equal.
View full question & answer→MCQ 601 Mark
Which of the following is true for the adjacent angles of a parallelogram?
- A
They are equal to each other
- B
They are complementary angles
- ✓
They are supplementary angles
- D
AnswerCorrect option: C. They are supplementary angles
Parallelogram: A parallelogram is a quadrilateral in which each pair of opposite sides is parallel. The two diagonals bisect each other. The pair of opposite sides is equal and the pair of opposite angles is equal.
Sum of the adjacent angles of a parallelogram is $180^\circ $.
i.e supplementary, $\angle{\text{A}}+\angle{\text{D}}=180^\circ$
Since, the adjacent angles of a parallelogram are supplementary angles. View full question & answer→MCQ 611 Mark
Which of the following figures satisfy the following property? $-$ Has two pairs of congruent adjacent sides.
AnswerWe know that, a kite has two pairs of congruent adjacent sides and we can observe that figure $R$ resembles a kite.
View full question & answer→MCQ 621 Mark
The sum of the internal angles of a polygon is $10$ right angles. Then the number of sides is:
Answer$(n - 2) 180^\circ = 10 \times 90^\circ $
$\Rightarrow n = 7.$
View full question & answer→MCQ 631 Mark
The diameter of circumcircle of a rectangle is $10\ cm$ and breath of the rectangle is $6\ cm$. Its length is:
- ✓
$8\ cm$
- B
$6\ cm$
- C
$5\ cm$
- D
AnswerCorrect option: A. $8\ cm$
$8\ cm$
View full question & answer→MCQ 641 Mark
In an isosceles parallelogram, we have:
AnswerCorrect option: B. Pair of non$-$parallel sides as equal
In Euclidean geometry, an isosceles trapezoid $($isosceles trapezium in British English$)$ is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides. Note that a non$-$rectangular parallelogram is not an isosceles trapezoid because of the second condition, or because it has no line of symmetry.
View full question & answer→MCQ 651 Mark
Tick the correct answer in the following? How many diagonals are there in a pentagon?
AnswerFor a pentagon:
$n = 5$
Number of diagonals $=\frac{\text{n}(\text{n}-3)}{2}=\frac{5(5-3)}{2}=5$
View full question & answer→MCQ 661 Mark
Tick the correct answer in the following? Each interior angle of a polygon is $135^\circ $. How many sides does it have?
AnswerEach interior angle for a regular polygon withn-sided $=180-\Big(\frac{360}{\text{n}}\Big)$
$180-\Big(\frac{360}{\text{n}}\Big)=135$
$\Rightarrow\Big(\frac{360}{\text{n}}\Big )=45$
$\Rightarrow\text{n}=8$
View full question & answer→MCQ 671 Mark
What is the sum of all the angles of a pentagon?
- A
$180^\circ$
- B
$360^\circ$
- ✓
$540^\circ$
- D
$720^\circ$
AnswerCorrect option: C. $540^\circ$
We know that, the sum of angles of a polygon is $(n - 2) \times 180^\circ ,$ where n is the number of sides of the polygon.
In pentagon, $n = 5$ Sum of the angles $= (n - 2) \times 180^\circ = (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ .$
View full question & answer→MCQ 681 Mark
Which of the following figures satisfy the following properties? All sides are congruent. All angles are right angles. Opposite sides are parallel.
AnswerWe know that all the properties mentioned above are related to square and we can observe that figure $R$ resembles a square.
View full question & answer→MCQ 691 Mark
In the quadrilateral $ABCD$, the diagonals $AC$ and $BD$ are equal and perpendicular to each other. Then $ABCD$ is a:
View full question & answer→MCQ 701 Mark
The angle sum of a convex polygon with number of sides $7$ is:
- ✓
$900^\circ$
- B
$1080^\circ$
- C
$1440^\circ$
- D
$720^\circ$
AnswerCorrect option: A. $900^\circ$
$n = 7$
$(n - 2) 180^\circ = 900^\circ$
View full question & answer→MCQ 711 Mark
A $.............$ is both ‘equiangular’ and ‘equilateral’.
View full question & answer→MCQ 721 Mark
The measures of each of the four angles of a quadrilateral are equal. Find the measure of each angle.
- A
$45^\circ$
- B
$30^\circ$
- C
$60^\circ$
- ✓
$90^\circ$
AnswerCorrect option: D. $90^\circ$
Measure of each angle
$= \frac{360^\circ}{4}=90^\circ$
View full question & answer→MCQ 731 Mark
Tick the correct answer in the following?
Each interior angle of a regular decagon is:
- A
$60^\circ$
- B
$120^\circ$
- ✓
$144^\circ$
- D
$180^\circ$
AnswerCorrect option: C. $144^\circ$
Each interior angle of a regular decagon $=180-\frac{360}{10}=180-36=144^\circ$
View full question & answer→MCQ 741 Mark
- A
Does not bisect each other
- B
- ✓
Are perpendicular to each other
- D
AnswerCorrect option: C. Are perpendicular to each other
The diagonals of a kite are perpendicular to each other. They intersect at $90$ degrees but does not bisect.
View full question & answer→MCQ 751 Mark
How many diagonals does a convex quadrilateral has?
AnswerA convex quadrilateral is a four sided figure with interior angles of less than $180$ degrees each and both of its diagonals contained within the shape. It has got two Diagonals.
View full question & answer→MCQ 761 Mark
The angle sum of a convex polygon with number of sides n is:
- ✓
$(n - 2) 180^\circ$
- B
$(n + 2) 180^\circ$
- C
$(2n - 4) 180^\circ $
- D
$(2n + 4) 180^\circ$
AnswerCorrect option: A. $(n - 2) 180^\circ$
$(n - 2) 180^\circ $
View full question & answer→MCQ 771 Mark
The measure of each exterior angle of a regular polygon of $9$ sides is:
- A
$30^\circ$
- ✓
$40^\circ$
- C
$60^\circ$
- D
$45^\circ$
AnswerCorrect option: B. $40^\circ$
Required measure $= \frac{360^\circ}{9}=40^\circ$
View full question & answer→MCQ 781 Mark
Which of the following figures do not satisfy any of the following properties? All sides are equal. All angles are right angles. Opposite sides are parallel.
AnswerOn observing the above figures, we conclude that the figure $P$ does not satisfy any of the given properties.
View full question & answer→MCQ 791 Mark
How many diagonals does a regular hexagon have?
MCQ 801 Mark
Which of the quadrilaterals has all angles as right angles, opposite sides equal and diagonals bisect$-$each other?
AnswerA rectangle is a quadrilateral in which all angles are right angles.
A rectangle is a parallelogram,
so its opposite sides are equal.
The diagonals of a rectangle are equal and bisect each other.
View full question & answer→MCQ 811 Mark
The sum of all exterior angles of a triangle is.
- A
$180^\circ$
- ✓
$360^\circ$
- C
$540^\circ$
- D
$720^\circ$
AnswerCorrect option: B. $360^\circ$
We know that the sum of exterior angles, taken in order of any polygon is $360^\circ $ and triangle is also a polygon. Hence, the sum of all exterior angles of a triangle is $360^\circ .$
View full question & answer→MCQ 821 Mark
How many sides does a regular polygon has if each of it's interior angle is $120^\circ ?$
AnswerLet assume polygon is regular polygon.
The measure of an interior angle, A, of a regular polygon of n sides is given by:
$\text{A}=\frac{\text{(n}-2)180^\circ} {\text{n}}$
$\Rightarrow120^\circ=\frac{\text{(n}-2)} {\text{n}}\times180^\circ.$
$\Rightarrow\frac{120^\circ\text{n}} {180^\circ}=\text{n}-2$
$\Rightarrow\frac{2} {\text{n}}=\text{n}-2$
$\Rightarrow\text{2n}=\text{3n}-6$
$\Rightarrow\text{n}=6$
$\therefore$ The regular polygon has 6 equal sides and is called a hexagon.
View full question & answer→MCQ 831 Mark
Which of the following statement is false?
- A
A square is a rectangle whose adjacent sides are equal.
- B
A square is a rhombus whose one angle is a right angle.
- C
The diagonals of a square bisect each other at right angles.
- ✓
The diagonals of a square do not divide the whole square into four equal parts.
AnswerCorrect option: D. The diagonals of a square do not divide the whole square into four equal parts.
The diagonals of a square do not divide the whole square into four equal parts.
View full question & answer→MCQ 841 Mark
Which of the following is true for the adjacent angles of a parallelogram?
- A
They are equal to each other
- B
They are complementary angles
- ✓
They are supplementary angles
- D
AnswerCorrect option: C. They are supplementary angles
They are supplementary angles
View full question & answer→MCQ 851 Mark
Find the perimeter of the rectangle $ABCD.$
- A
$6\ cm$
- ✓
$12\ cm$
- C
$3\ cm$
- D
$24\ cm$
AnswerCorrect option: B. $12\ cm$
Perimeter $= 2 (4 + 2)cm = 12cm.$
View full question & answer→MCQ 861 Mark
What is the minimum interior angle possible for a regular polygon?
- ✓
$60^\circ$
- B
$80^\circ$
- C
$120^\circ $
- D
$160^\circ$
AnswerCorrect option: A. $60^\circ$
Since on increasing the size of regular polygon $\Rightarrow $ its angle increase.
Minimum interior angle for regular triangle. i.e. equilateral triangle and Minimum interior angle $= 60^\circ $
View full question & answer→MCQ 871 Mark
What is the maximum number of obtuse angles that a quadrilateral can have?
AnswerWe know that, the sum of all the angles of a quadrilateral is $360^\circ $. Also, an obtuse angle is more than 90^\circ and less than $180^\circ $.
View full question & answer→MCQ 881 Mark
If two adjacent angles of a parallelogram are in the ratio $3 : 2$, then the measure of the angles are:
- A
$100^\circ , 80^\circ $
- B
$72^\circ , 36^\circ$
- ✓
$108^\circ , 72^\circ$
- D
$144^\circ , 36^\circ$
AnswerCorrect option: C. $108^\circ , 72^\circ$
$108^\circ , 72^\circ$
View full question & answer→MCQ 891 Mark
In the figure, $BEST$ is a rhombus, Then the value of $y – x$ is:
- ✓
$40^\circ$
- B
$50^\circ$
- C
$20^\circ$
- D
$10^\circ$
AnswerCorrect option: A. $40^\circ$
Given, a rhombus BEST ??|| ?? and ?? is transversal.
$\therefore\angle\text{SBE}=\angle\text{TSB}=40^\circ$
Also, y = $90^\circ$
In $\triangle\text{TSO}, \angle\text{STO}+\angle\text{TOS}=\angle\text{SOE}$
$\Rightarrow \text{x}+40^\circ+90^\circ $
$\Rightarrow\text{x}=50^\circ$
$\Rightarrow\text{y}-\text{x}=90^\circ-50^\circ=40^\circ$
View full question & answer→MCQ 901 Mark
Two adjacent angles of a parallelogram are $(2x + 25)^\circ $ and $(3x - 5)^\circ $. The value of $x$ is:
Answer$\therefore (2x + 25) + (3x - 5) = 180$
$\Rightarrow 2x + 25 + 3x - 5 = 180$
$\Rightarrow 5x = 180 - 20$
$\Rightarrow 5x = 160$
$\Rightarrow x = 32$
View full question & answer→MCQ 911 Mark
If the length of a side of a rhombus is $6\ cm$, then the perimeter of the rhombus is:
- A
$6\ cm$
- B
$12\ cm$
- ✓
$24\ cm$
- D
$3\ cm$
AnswerCorrect option: C. $24\ cm$
Perimeter $= 4$ side
$= 4 \times 6 = 24cm$
View full question & answer→MCQ 921 Mark
If two adjacent angles of a parallelogram are in the ratio $2 : 3,$ then the measure of angles are:
- ✓
$72^\circ, 108^\circ$
- B
$36^\circ, 54^\circ$
- C
$80^\circ, 120^\circ$
- D
$96^\circ, 144^\circ$
AnswerCorrect option: A. $72^\circ, 108^\circ$
A. $72^\circ, 108^\circ$
Solution:
Let the angles be $2x$ and $3x.$ Then, $2x + 3x = 180^\circ$ [adjacent angles of a parallelogram are supplementary]
$\Rightarrow 5x = 180^\circ$
$\Rightarrow x = 36^\circ$
Hence, the measures of angles are $2x = 2 \times 36^\circ = 72^\circ$ and $3x = 3 \times 36^\circ = 108^\circ$
View full question & answer→MCQ 931 Mark
If angles $P, Q, R$ and $S$ of the quadrilateral $PQRS$, taken in order, are in the ratio $3:7:6:4$ then $PQRS$ is a:
View full question & answer→MCQ 941 Mark
Tick the correct answer in the following? A polygon has $27$ diagonals. How many sides does it have?
Answer$\frac{\text{n}(\text{n}-3)}{2}=27$
$\Rightarrow(\text{n}-3)=54$
$\Rightarrow\text{n}^2-3\text{n}-54=0$
$\Rightarrow\text{n}^2-9\text{n}+6\text{n}-54=0$
$\Rightarrow\text{n}(\text{n}-9)+6(\text{n}-9)=0$
$\Rightarrow\text{n}=-6\ \text{or}\ \text{n}=9$
Number of sides cannot be negative.
$\therefore\text{n}=9$
View full question & answer→MCQ 951 Mark
The diagonals do not necessarily bisect the interior angles at the vertices in a:
AnswerIn rectangle, only opposite sides are equal which makes diagonals are not to be perpendicular to each other. As diagonals are not perpendicular to each other, they will not bisect the interior angles.
View full question & answer→MCQ 961 Mark
The measure of each exterior angle of a regular polygon of $15$ sides is:
- A
$30^\circ$
- B
$45^\circ$
- C
$60^\circ$
- ✓
$24^\circ$
AnswerCorrect option: D. $24^\circ$
Required measure $= \frac{360^\circ}{15}=24^\circ$
View full question & answer→MCQ 971 Mark
A quadrilateral has three acute angles. If each measures $80^\circ $, then the measure of the fourth angle is.
- A
$150^\circ$
- ✓
$120^\circ$
- C
$105^\circ$
- D
$140^\circ$
AnswerCorrect option: B. $120^\circ$
Let the fourth angle be $x.$
$80^\circ+80^\circ+80^\circ\ \text{x}^\circ=360^\circ$
$\Rightarrow240^\circ+\text{x}=360^\circ$
$\Rightarrow\text{x}=360^\circ-240^\circ$
$\Rightarrow\text{x}=120^\circ$
View full question & answer→MCQ 981 Mark
Which of the following statement is false?
- A
All the rectangles are parallelograms.
- B
All the squares are rectangles.
- ✓
All the parallelograms are rectangles.
- D
All the rhombuses are parallelograms.
AnswerCorrect option: C. All the parallelograms are rectangles.
All the parallelograms are rectangles.
View full question & answer→MCQ 991 Mark
Two adjacent sides of a rectangle are equal. The name of the quadrilateral is:
MCQ 1001 Mark
Tick the correct answer in the following? How many diagonals are there in a hexagon?
AnswerNumber of diagonals in an n-sided polygon $=\frac{\text{n}(\text{n}-3)}{2}$
$\text{n}=6$
$\therefore\frac{\text{n}(\text{n}-3)}{2}=\frac{6(6-3}{2}$
$=\frac{18}{9}=9$
View full question & answer→
