Question 11 Mark
Every rectangle is a trapezium.
Answer
View full question & answer→True. Solution: As a rectangle satisfies all the properties of a trapezium. So, we can say that, every rectangle is a trapezium but vice-versa is not true.
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Question 21 Mark
Three angles of a quadrilateral are equal. Fourth angle is of measure $120^\circ .$ What is the measure of equal angles$?$
Answer
View full question & answer→Let the measures of angles be $x^\circ $ each.
Then, by the angle sum property of a quadrilateral,
$x^\circ + x^\circ + x^\circ + 120^\circ = 360^\circ $
$\Rightarrow 3x^\circ + 120^\circ = 360^\circ $
$\Rightarrow 3x^\circ = 360^\circ - 120^\circ $
$\Rightarrow\frac{240^\circ}{3}=80^\circ$
Then, by the angle sum property of a quadrilateral,
$x^\circ + x^\circ + x^\circ + 120^\circ = 360^\circ $
$\Rightarrow 3x^\circ + 120^\circ = 360^\circ $
$\Rightarrow 3x^\circ = 360^\circ - 120^\circ $
$\Rightarrow\frac{240^\circ}{3}=80^\circ$
Question 31 Mark
Adjacent angles of a parallelogram are _____.
Answer
View full question & answer→Adjacent angles of a parallelogram are supplementary. Solution: By property of a parallelogram, we know that, the adjacent angles of a parallelogram are supplementary.
Question 41 Mark
Diagonals of a rhombus are equal and perpendicular to each other.
Answer
View full question & answer→False. Solution: As diagonals of a rhombus are perpendicular to each other but not equal.
Question 51 Mark
If all sides of a quadrilateral are equal, it is a _____.
Answer
View full question & answer→ If all sides of a quadrilateral are equal, it is a rhombus or square.
Solution:
As in both the quadrilaterals all sides are of equal length.
Solution:
As in both the quadrilaterals all sides are of equal length.
Question 61 Mark
If the sum of interior angles is double the sum of exterior angles taken in an order of a polygon, then it is a hexagon.
Answer
View full question & answer→True. Solution: Since the sum of exterior angles of a hexagon is $360^\circ$ and the sum of interior angles of a hexagon is $720^\circ$ , i.e. double the sum of exterior angles.
Question 71 Mark
In trapezium $ABCD$ with $AB || CD,$ if $\angle\text{A}=100^\circ, \text{then}\ \angle\text{D}=$ _____.
Answer
View full question & answer→In trapezium $ABCD$ with $AB || CD,$
if $\angle\text{A}=100^\circ, \text{then}\ \angle\text{D}= 80^\circ .$
Solution: In trapezium, we know that, the angles on either sides of the base are supplementary.
So, in trapezium $ABCD,$ given $?? || ??$
$\therefore\angle\text{A}+\angle\text{D}=180^\circ$
$\Rightarrow100^\circ+\angle\text{D}\ 180^\circ$
$\Rightarrow\angle\text{D}=180^\circ-100^\circ$
$\Rightarrow\angle\text{D}=80^\circ$
if $\angle\text{A}=100^\circ, \text{then}\ \angle\text{D}= 80^\circ .$
Solution: In trapezium, we know that, the angles on either sides of the base are supplementary.
So, in trapezium $ABCD,$ given $?? || ??$
$\therefore\angle\text{A}+\angle\text{D}=180^\circ$
$\Rightarrow100^\circ+\angle\text{D}\ 180^\circ$
$\Rightarrow\angle\text{D}=180^\circ-100^\circ$
$\Rightarrow\angle\text{D}=80^\circ$
Question 81 Mark
A nonagon has _____ sides.
Answer
View full question & answer→A nonagon has $9$ sides. Solution: Nonagon is a polygon which has $9$ sides.
Question 91 Mark
In quadrilateral $WXYZ,$ the pairs of opposite angles are _____.
Answer
View full question & answer→In quadrilateral $WXYZ,$ the pairs of opposite angles are $\angle\text{w}, \angle\text{y}; \angle\text{x}, \angle\text{z}.$
Solution:
The pairs of opposite angles are.
Solution:
The pairs of opposite angles are.
Question 101 Mark
Every square is a trapezium.
Answer
View full question & answer→True. Solution: As a square has all the properties of a trapezium. So, we can say that, every square is a trapezium but vice-versa is not true.
Question 111 Mark
A rectangle whose adjacent sides are equal becomes a _____.
Answer
View full question & answer→A rectangle whose adjacent sides are equal becomes a square. Solution: If in a rectangle, adjacent sides are equal, then it is called a square.
Question 121 Mark
If diagonals of a quadrilateral bisect each other, it must be a parallelogram.
Answer
View full question & answer→True. Solution: It is the property of a parallelogram.
Question 131 Mark
The measure of _____ angle of concave quadrilateral is more than $180^\circ .$
Answer
View full question & answer→The measure of one angle of concave quadrilateral is more than $180^\circ$.
Solution:
Concave polygon is a polygon in which at least one interior angle is more than $180^\circ$.
Solution:
Concave polygon is a polygon in which at least one interior angle is more than $180^\circ$.
Question 141 Mark
A rhombus can be constructed uniquely if both diagonals are given.
Answer
View full question & answer→True. Solution: A rhombus can be constructed uniquely, if both diagonals are given.
Question 151 Mark
A polygon is a simple closed curve made up of only _____.
Answer
View full question & answer→A polygon is a simple closed curve made up of only line segments. Solution: since a simple closed curve made up of only line segments is called a polygon.
Question 161 Mark
A quadrilateral can be drawn if only measures of four sides are given.
Answer
View full question & answer→False. Solution: As we require at least five measurements to determine a quadrilateral uniquely.
Question 171 Mark
quadrilateral has two diagonals.
Answer
View full question & answer→As the sum of interior angles of a triangle is $180^\circ $ and the sum of exterior angles is $360^\circ ,$ i.e. double the sum.
Question 181 Mark
The sum of all _____ of a quadrilateral is $360^\circ $
Answer
View full question & answer→The sum of all angles of a quadrilateral is $360^\circ$
Solution:
We know that, the sum of all angles of a quadrilateral is $360^\circ$.
Solution:
We know that, the sum of all angles of a quadrilateral is $360^\circ$.
Question 191 Mark
_____ measurements can determine a quadrilateral uniquely.
Answer
View full question & answer→$5$ measurements can determine a quadrilateral uniquely.
Solution: To construct a unique quadrilateral, we require $5$ measurements,
i.e. four sides and one angle or three sides and two included angles or two adjacent sides and three angles are given.
Solution: To construct a unique quadrilateral, we require $5$ measurements,
i.e. four sides and one angle or three sides and two included angles or two adjacent sides and three angles are given.
Question 201 Mark
Sum of the angles of a hexagon is _____.
Answer
View full question & answer→Sum of the angles of a hexagon is $720^\circ .$
Solution:
Since, the sum of angles of an $n-$gon $= (n − 2) \times 180^\circ$
$\therefore $ Sum of the angles of a hexagon $= (6 − 2) \times 180^\circ = 4 \times 180^\circ =720^\circ$
Solution:
Since, the sum of angles of an $n-$gon $= (n − 2) \times 180^\circ$
$\therefore $ Sum of the angles of a hexagon $= (6 − 2) \times 180^\circ = 4 \times 180^\circ =720^\circ$
Question 211 Mark
The number of diagonals in a hexagon is _____.
Answer
View full question & answer→The number of diagonals in a hexagon is equilateral triangle. Solution: as polygon is regular, i.e. length of each side is same.
Question 221 Mark
_____is a regular quadrilateral.
Answer
View full question & answer→Square is a regular quadrilateral. Solution: Since in square, all the sides are of equal length and all angles are equal.
Question 231 Mark
A quadrilateral has two diagonals.
Answer
View full question & answer→True. Solution: A quadrilateral has two diagonals.
Question 241 Mark
The sum of all exterior angles of a polygon is _____.
Answer
View full question & answer→The sum of all exterior angles of a polygon is $360^\circ .$
Solution: As the sum of all exterior angles of a polygon is $360^\circ .$
Solution: As the sum of all exterior angles of a polygon is $360^\circ .$
Question 251 Mark
All angles of a trapezium are equal.
Answer
View full question & answer→False. Solution: As all angles of a trapezium are not equal.
Question 261 Mark
Sum of all the angles of a quadrilateral is $180^\circ .$
Answer
View full question & answer→False. Solution: Since sum of all the angles of a quadrilateral is $360^\circ .$
Question 271 Mark
Rectangle is a regular quadrilateral.
Answer
View full question & answer→False. Solution: As its all sides are not equal.
Question 281 Mark
A polygon having $10$ sides is known as _____.
Answer
View full question & answer→A polygon having $10$ sides is known as $5.$
Solution: We know that, the sum of exterior angles of any polygon is $360^\circ .$
Solution: We know that, the sum of exterior angles of any polygon is $360^\circ .$
Question 291 Mark
Diagonals of a rectangle are _____.
Answer
View full question & answer→Diagonals of a rectangle are equal. Solution: We know that, in a rectangle, both the diagonals are of equal length.
Question 301 Mark
The measure of each exterior angle of a regular pentagon is _____.
Answer
View full question & answer→The measure of each exterior angle of a regular pentagon is $78^\circ .$
Solution: Measures of exterior angle $=\frac{360^\circ}{\text{Number of sides}}=\frac{360^\circ}{5}=72^\circ.$
Solution: Measures of exterior angle $=\frac{360^\circ}{\text{Number of sides}}=\frac{360^\circ}{5}=72^\circ.$
Question 311 Mark
In a rhombus diagonals intersect at _____ angles.
Answer
View full question & answer→In a rhombus diagonals intersect at right angles.solution:
The diagonals of a rhombus intersect at right angles.
The diagonals of a rhombus intersect at right angles.
Question 321 Mark
In quadrilateral $HOPE,$ the pairs of opposite sides are _____.
Answer
View full question & answer→In quadrilateral $HOPE,$ the pairs of opposite sides are $EH, PO$ and $HO, EP.$
Solution:
are pairs of opposite sides.
Solution:
are pairs of opposite sides.
Question 331 Mark
A quadrilateral can be drawn if three sides and two diagonals are given.
Answer
View full question & answer→True. Solution: A quadrilateral can be drawn, if three sides and two diagonals are given.
Question 341 Mark
Every rhombus is a trapezium.
Answer
View full question & answer→ True.
Solution:
Since a rhombus satisfies all the properties of a trapezium. So, we can say that, every rhombus is a trapezium but vice-versa is not true.
Solution:
Since a rhombus satisfies all the properties of a trapezium. So, we can say that, every rhombus is a trapezium but vice-versa is not true.
Question 351 Mark
The measure of each exterior angle of a regular polygon of $18$ sides is _____.
Answer
View full question & answer→The measure of each exterior angle of a regular polygon of $18$ sides is $20^\circ .$
Solution: We know that, measure of each exterior angle $=\frac{360^\circ}{\text{Number of sides}}=\frac{360^\circ}{18}=20^\circ.$
Solution: We know that, measure of each exterior angle $=\frac{360^\circ}{\text{Number of sides}}=\frac{360^\circ}{18}=20^\circ.$
Question 361 Mark
A quadrilateral in which a pair of opposite sides is parallel is_____.
Answer
View full question & answer→ A quadrilateral in which a pair of opposite sides is parallel is trapezium.
Solution:
We know that, in a trapezium, one pair of sides is parallel.
Solution:
We know that, in a trapezium, one pair of sides is parallel.
Question 371 Mark
A parallelogram can be constructed uniquely if both diagonals and the angle between them is given.
Answer
View full question & answer→True. Solution: We can draw a unique parallelogram, if both diagonals and the angle between them is given.
Question 381 Mark
If only one diagonal of a quadrilateral bisects the other, then the quadrilateral is known as _____.
Answer
View full question & answer→ If only one diagonal of a quadrilateral bisects the other, then the quadrilateral is known as kite.
Solution:
This is a property of kite, i.e., only one diagonal bisects the other.
Solution:
This is a property of kite, i.e., only one diagonal bisects the other.
Question 391 Mark
Diagonals of a rectangle are equal.
Answer
View full question & answer→True. Solution: The diagonals of a rectangle are equal.
Question 401 Mark
The number of sides of a regular polygon, where each exterior angle has a measure of $36^\circ$, is _____.
Answer
View full question & answer→The number of sides of a regular polygon, where each exterior angle has a measure of $36^\circ ,$ is $10^\circ .$
Solution: The sum of exterior angles of a regular polygon is $360^\circ$ Further, since each exterior angle is of $36^\circ ,$ therefore, number of sides $=\frac{360^\circ}{\text{Exterior angle}}=\frac{360^\circ}{36^\circ}=10^\circ.$
Solution: The sum of exterior angles of a regular polygon is $360^\circ$ Further, since each exterior angle is of $36^\circ ,$ therefore, number of sides $=\frac{360^\circ}{\text{Exterior angle}}=\frac{360^\circ}{36^\circ}=10^\circ.$
Question 411 Mark
Every kite is a parallelogram.
Answer
View full question & answer→False. Solution: Kite is not a parallelogram as its opposite sides are not equal and parallel.
Question 421 Mark
If opposite angles of a quadrilateral are equal, it must be a parallelogram.
Answer
View full question & answer→True. Solution: If opposite angles are equal, it has to be a parallelogram.
Question 431 Mark
The polygon in which sum of all exterior angles is equal to the sum of interior angles is called _____.
Answer
View full question & answer→The polygon in which sum of all exterior angles is equal to the sum of interior angles is called quadrilateral.
Solution:
We know that, the sum of exterior angles of a polygon is $360^\circ $ and in a quadrilateral, sum of interior angles is also $360^\circ .$ Therefore, a quadrilateral is a polygon in which the sum of both interior and exterior angles are equal.
Solution:
We know that, the sum of exterior angles of a polygon is $360^\circ $ and in a quadrilateral, sum of interior angles is also $360^\circ .$ Therefore, a quadrilateral is a polygon in which the sum of both interior and exterior angles are equal.
Question 441 Mark
A regular polygon is a polygon whose all sides are equal and all _____are equal.
Answer
View full question & answer→A regular polygon is a polygon whose all sides are equal and all angles In a regular polygon, are equal. Solution: all sides are equal and all angles are equal.
Question 451 Mark
The adjacent sides of a parallelogram are $5\ cm$ and $9\ cm.$ Its perimeter is _____.
Answer
View full question & answer→The adjacent sides of a parallelogram are $5\ cm$ and $9\ cm.$ Its perimeter is $28\ cm.$
Solution: Perimeter of a parallelogram $= 2 ($Sum of lengths of adjacent sides$) = 2(5 + 9) = 2 \times 14 = 28\ cm$
Solution: Perimeter of a parallelogram $= 2 ($Sum of lengths of adjacent sides$) = 2(5 + 9) = 2 \times 14 = 28\ cm$
Question 461 Mark
Every trapezium is a parallelogram.
Answer
View full question & answer→False. Solution: Since in a trapezium, only one pair of sides is parallel.
Question 471 Mark
A quadrilateral can be drawn when all the four angles and one side is given.
Answer
View full question & answer→ False.
Solution:
We cannot draw a unique-quadrilateral, if four angles and one side is known.
Solution:
We cannot draw a unique-quadrilateral, if four angles and one side is known.
Question 481 Mark
All rhombuses are squares.
Answer
View full question & answer→ False.
Solution:
As in a rhombus, each angle is not a right angle, so rhombuses are not squares.
Solution:
As in a rhombus, each angle is not a right angle, so rhombuses are not squares.
Question 491 Mark
A quadrilateral can have all four angles as obtuse.
Answer
View full question & answer→False. Solution: If all angles will be obtuse, then their sum will exceed $360^\circ .$ This is not possible in case of a quadrilateral.
Question 501 Mark
The name of three-sided regular polygon is _____.
Answer
View full question & answer→The name of three-sided regular polygon is equilateral triangle. Solution: as polygon is regular, i.e. length of each side is same.