Rs Aggarwal 2017 Solutions for Class 8 Math Chapter 17 Construction Of Quadrilaterals are provided here with simple step-by-step explanations. These solutions for Construction Of Quadrilaterals are extremely popular among Class 8 students for Math Construction Of Quadrilaterals Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2017 Book of Class 8 Math Chapter 17 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2017 Solutions. All Rs Aggarwal 2017 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

#### Question 1:

Construct a quadrilateral ABCD in which AB = 4.2 cm, BC = 6 cm, CD = 5.2 cm, DA = 5 cm and AC = 8 cm.

Steps of construction:
Step 1: Draw .
Step 2: With A as the centre and radius equal to , draw an arc.
Step 3: With B as the centre and radius equal to , draw another arc, cutting the previous arc at C.
Step 4: Join BC.
Step 5: With A as the centre and radius equal to  draw an arc.
Step 6: With C as the centre and radius equal to , draw another arc, cutting the previous arc at D.
Step 7: Join AD and CD.

Thus, ABCD is the required quadrilateral.

#### Question 2:

Construct a quadrilateral PQRS in which PQ = 5.4 cm, QR = 4.6 cm, RS = 4.3 cm, SP = 3.5 cm and diagonal PR = 4 cm.

Steps of construction:
Step 1: Draw .
Step 2: With P as the centre and radius equal to , draw an arc.
Step 3: With Q as the centre and radius equal to , draw another arc, cutting the previous arc at R.
Step 4: Join QR.
Step 5: With P as the centre and radius equal to  draw an arc.
Step 6: With R as the centre and radius equal to , draw another arc, cutting the previous arc at S.
Step 7: Join PS and RS.

Thus, PQRS is the required quadrilateral.

#### Question 3:

Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 3.8 cm, CD = DA = 4.5 cm and diagonal BD = 5.6 cm.

Steps of construction:
Step 1: Draw .
Step 2: With B as the centre and radius equal to , draw an arc.
Step 3: With A as the centre and radius equal to , draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With D as the centre and radius equal to  draw an arc.
Step 6: With B as the centre and radius equal to , draw another arc, cutting the previous arc at C.
Step 7: Join BC and CD.

Thus, ABCD is the required quadrilateral.

#### Question 4:

Construct a quadrilateral ABCD in which AB = 3.6 cm, BC = 3.3 cm, AD = 2.7 cm, diagonal AC = 4.6 cm and diagonal BD = 4 cm.

Steps of construction:
Step 1: Draw .
Step 2: With B as the centre and radius equal to , draw an arc.
Step 3: With A as the centre and radius equal to , draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With A as the centre and radius equal to  draw an arc.
Step 6: With B as the centre and radius equal to , draw another arc, cutting the previous arc at C.
Step 7: Join AC, BC and CD.

Thus, ABCD is the required quadrilateral.

#### Question 5:

Construct a quadrilateral PQRS in which QR = 7.5 cm, PR = PS = 6 cm, RS = 5 cm and QS = 10 cm. Measure the fourth side.

Steps of construction:
Step 1: Draw
Step 2: With Q as the centre and radius equal to , draw an arc.
Step 3: With R as the centre and radius equal to , draw another arc, cutting the previous arc at S.
Step 4: Join QS and RS.
Step 5: With S as the centre and radius equal to  draw an arc.
Step 6: With R as the centre and radius equal to , draw another arc, cutting the previous arc at P.
Step 7: Join PS and PR.
Step 8: PQ = 4.9 cm
Thus, PQRS is the required quadrilateral.

#### Question 6:

construct a quadrilateral ABCD in which AB =3.4 cm, CD = 3 cm, DA = 5.7 cm, AC = 8 cm and BD = 4 cm.

Steps of construction:
Step 1: Draw
Step 2: With B as the centre and radius equal to , draw an arc.
Step 3: With A as the centre and radius equal to , draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With A as the centre and radius equal to  draw an arc.
Step 6: With D as the centre and radius equal to , draw another arc, cutting the previous arc at C.
Step 7: Join AC, CD and BC.

Thus, ABCD is the required quadrilateral.

#### Question 7:

Construct a quadrilateral ABCD in which AB = BC = 3.5 cm, AD = CD = 5.2 cm and ∠ABC = 120°.

Steps of construction:
Step 1: Draw AB.
Step 2: Make $\angle ABC={120}^{\circ }$.
Step 3: With B as the centre, draw an arc  and name that point C.
Step 4: With C as the centre, draw an arc .
Step 5: With A as the centre, draw another arc ​, cutting the previous arc at D.
Step 6: Join CD and AD.
Thus, $ABCD$ is the required quadrilateral.

#### Question 8:

Construct a quadrilateral ABCD in which AB = 2.9 cm, BC = 3.2 cm, CD = 2.7 cm, DA = 3.4 cm and ∠A = 70°.

Steps of construction:
Step 1: Draw AB$2.9cm$
Step 2: Make $\angle A={70}^{\circ }$
Step 3: With A as the centre, draw an arc of $3.4cm$. Name that point as D.
Step 4: With D as the centre, draw an arc of $2.7cm$.
Step 5: With B as the centre, draw an arc of 3.2 cm, cutting the previous arc at C.
Step 6: Join CD and BC.
Then, $ABCD$ is the required quadrilateral.

#### Question 9:

Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 5 cm, CD = 4.6 cm, ∠B = 125° and ∠C = 60°.

Steps of construction:
Step 1: Draw BC$5cm$
Step 2: Make
Step 3: With B as the centre, draw an arc of . Name that point as A.
Step 4: With C as the centre, draw an arc of . Name that point as D.
Step 5: Join A and D.
Then, $ABCD$ is the required quadrilateral.

#### Question 10:

Construct a quadrilateral PQRS in which PQ = 6 cm, QR = 5.6 cm, RS = 2.7 cm, ∠Q = 45° and ∠R = 90°.

Steps of construction:
Step 1: Draw QR
Step 2: Make
Step 3: With Q as the centre, draw an arc of . Name that point as P.
Step 4: With R as the centre, draw an arc of $2.7cm$. Name that point as S.
Step 6: Join P and S.
Then, $PQRS$ is the required quadrilateral.

#### Question 11:

Construct a quadrilateral ABCD in which AB = 5.6 cm, BC = 4 cm, ∠A = 50°, ∠B = 105° and ∠D = 80°.

Steps of construction:
Step 1: Draw AB
Step 2: Make
Step 3: With B as the centre, draw an arc of $4cm$.
Step 3: Sum of all the angles of the quadrilateral is ${360}^{\circ }$.
$\angle A+\angle B+\angle C+\angle D={360}^{\circ }\phantom{\rule{0ex}{0ex}}{50}^{\circ }+{105}^{\circ }+\angle C+{80}^{\circ }={360}^{\circ }\phantom{\rule{0ex}{0ex}}{235}^{\circ }+\angle C={360}^{\circ }\phantom{\rule{0ex}{0ex}}\angle C={360}^{\circ }-{235}^{\circ }\phantom{\rule{0ex}{0ex}}\angle C={125}^{\circ }$
Step 5: With C as the centre, make .
Step 6: Join C and D.
Step 7: Measure $\angle D={80}^{\circ }$
Then, $ABCD$ is the required quadrilateral.

#### Question 12:

Construct a quadrilateral PQRS in which PQ = 5 cm, QR = 6.5 cm, ∠P = ∠R = 100° and ∠S = 75°.

Steps of construction:
Step 1: Draw PQ$5cm$
Step 2:
$\angle P+\angle Q+\angle R+\angle S={360}^{\circ }\phantom{\rule{0ex}{0ex}}{100}^{\circ }+\angle Q+{100}^{\circ }+{75}^{\circ }={360}^{\circ }\phantom{\rule{0ex}{0ex}}{275}^{\circ }+\angle Q={360}^{\circ }\phantom{\rule{0ex}{0ex}}\angle Q={360}^{\circ }-{275}^{\circ }\phantom{\rule{0ex}{0ex}}\angle Q={85}^{\circ }$
Step 3: Make
Step 3: With Q as the centre, draw an arc of .
Step 4: Make $\angle R={100}^{\circ }$
Step 6: Join R and S.
Step 7: Measure $\angle S={75}^{\circ }$
Then, $PQRS$ is the required quadrilateral.

#### Question 13:

Construct a quadrilateral ABCD in which AB = 4 cm, AC = 5 cm, AD = 5.5 cm and ∠ABC = ∠ACD = 90°.

Steps of construction:
Step 1: Draw $AB=4cm$
Step 2:
Step 3: $A{C}^{2}=A{B}^{2}+B{C}^{2}\phantom{\rule{0ex}{0ex}}{5}^{2}={4}^{2}+B{C}^{2}\phantom{\rule{0ex}{0ex}}25-16=B{C}^{2}\phantom{\rule{0ex}{0ex}}BC=3cm$
With B as the centre, draw an arc equal to 3 cm.
Step 4: Make $\angle C={90}^{\circ }$
Step 5: With A as the centre and radius equal to , draw an arc and name that point as D.
Then, $ABCD$ is the required quadrilateral.

#### Question 1:

Construct a parallelogram ABCD in which AB = 5.2 cm, BC = 4.7 cm and AC = 7.6 cm.

Steps of construction:
Step 1: Draw AB $5.2cm$
Step 2: With B as the centre, draw an arc of .
Step 3: With A as the centre, draw another arc of , cutting the previous arc at C.
Step 4: Join A and C.
Step 5: We know that the opposite sides of a parallelogram are equal. Thus, with C as the centre, draw an arc of $5.2cm$.
Step 6: With A as the centre, draw another arc of , cutting the previous arc at D.
Step 7: Join CD and AD.
Then, ABCD is the required parallelogram.

#### Question 2:

Construct a parallelogram ABCD in which AB = 4.3 cm, AD = 4 cm and BD = 6.8 cm.

Steps of construction:
Step 1: Draw AB= $4.3cm$
Step 2: With B as the centre, draw an arc of .
Step 3: With A as the centre, draw another arc of $4cm$, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: We know that the opposite sides of a parallelogram are equal.
Thus, with D as the centre, draw an arc of $4.3cm$.
Step 6: With B as the centre, draw another arc of , cutting the previous arc at C.
Step 7: Join CD and BC.
​then, ABCD is the required parallelogram.

#### Question 3:

Construct a parallelogram PQRS in which QR = 6 cm, PQ = 4 cm and ∠PQR = 60° cm.

Steps of construction:
Step 1: Draw PQ= 4 cm
Step 2: Make $\angle PQR={60}^{\circ }$
Step 2: With Q as the centre, draw an arc of 6 cm and name that point as R.
Step 3: With R as the centre, draw an arc of 4 cm and name that point as S.
Step 4: Join SR and PS.
Then, PQRS is the required parallelogram.

#### Question 4:

Construct a parallelogram ABCD in which BC = 5 cm, ∠BCD = 120° and CD = 4.8 cm.

Steps of construction:
Step 1: Draw BC= $5cm$
Step 2: Make an $\angle BCD={120}^{\circ }$
Step 2: With C as centre draw an arc of , name that point as D
Step 3: With D as centre draw an arc $5\mathrm{cm}$, name that point as A
Step 4: With B as centre draw another arc  cutting the previous arc at A.
Step 5: Join AD and AB
​then, ABCD is a required parallelogram.

#### Question 5:

Construct a parallelogram, one of whose sides is 4.4 cm and whose diagonals are 5.6 cm and 7 cm. Measure the other side.

We know that the diagonals of a parallelogram bisect each other.
Steps of construction:
Step 1: Draw AB$4.4cm$
Step 2: With A as the centre and radius $2.8cm$, draw an arc.
Step 3: With B as the centre and radius $3.5cm$, draw another arc, cutting the previous arc at point O.
Step 4: Join OA and OB.
Step 5: Produce OA to C, such that OC= AO. Produce OB to D, such that OB=OD.
Step 5: Join AD, BC, and CD.
Thus, ABCD is the required parallelogram. The other side is 4.5 cm in length.

#### Question 6:

Construct a parallelogram ABCD in which AB = 6.5 cm, AC = 3.4 cm and the altitude AL from A is 2.5 cm. Draw the altitude from C and measure it.

Steps of construction:
Step 1: Draw AB= 6.5cm
Step 2: Draw a perpendicular at point A. Name that ray as AX. From point A, draw an arc of length 2.5 cm on the ray AX and name that point as L.
Step 3: On point L, make a perpendicular. Draw a straight line YZ passing through L, which is perpendicular to the ray AX.
Step 4: Cut an arc of length 3.4 cm on the line YZ and name it as C.
Step 5: From point C, cut an arc of length 6.5 cm on the line YZ. Name that point as D.
Step 6: Join BC and AD.

Therefore, quadrilateral ABCD is a parallelogram.

The altitude from C measures 2.5 cm in length.

#### Question 7:

Construct a parallelogram ABCD, in which diagonal AC = 3.8 cm, diagonal BD = 4.6 cm and the angle between AC and BD is 60°.

We know that the diagonals of a parallelogram bisect each other.

Steps of construction:
Step 1: Draw AC$3.8\mathrm{cm}$
Step 2: Bisect AC at O.
Step 3: Make $\angle COX={60}^{\circ }$
Produce XO to Y.
Step 4:

Step 5: Join AB, BC, CD and AD.
​Thus, ABCD is the required parallelogram.

#### Question 8:

Construct a rectangle ABCD whose adjacent sides are 11 cm and 8.5 cm.

Steps of construction:
Step 1: Draw AB = $11cm$
Step 2: Make
Step 3: Draw an arc of 8.5 cm from point A and name that point as D.
Step 4: Draw an arc of 8.5 cm from point B and name that point as C.
Step 5: Join C and D.
Thus, ABCD is the required rectangle.

#### Question 9:

Construct a square, each of whose sides measures 6.4 cm.

All the sides of a square are equal.
Steps of construction:
Step 1: Draw AB $6.4cm$
Step 2: Make
Step 3: Draw an arc of length 6.4 cm from point A and name that point as D.
Step 4: Draw an arc of length 6.4 cm from point B and name that point as C.
Step 5: Join C and D.
​Thus, ABCD is a required square.

#### Question 10:

Construct a square, each of whose diagonals measures 5.8 cm.

We know that the diagonals of a square bisect each other at right angles.
Steps of construction:
Step 1: Draw AC
Step 2: Draw the perpendicular bisector XY of AC, meeting it at O.
Step 3:

Step 4: Join AB, BC, CD and DA.
ABCD is the required square.

#### Question 11:

Construct a rectangle PQRS in which QR = 3.6 cm and diagonal PR = 6 cm. Measure the other side of the rectangle.

Steps of construction:
Step 1: Draw QR$3.6cm$
Step 2: Make  $\angle Q={90}^{\circ }\phantom{\rule{0ex}{0ex}}\angle R={90}^{\circ }$
Step 3:

Step 3: Draw an arc of length 4.8 cm from point Q and name that point as P.
​Step 4: Draw an arc of length 6 cm from point R, cutting the previous arc at P.
​Step 5: Join PQ
Step 6: Draw an arc of length 4.8 cm from point R.
F
rom point P, draw an arc of length 3.6 cm, cutting the previous arc. Name that point as S.
Step 7: Join P and S.
Thus, PQRS is the required rectangle. The other side is 4.8 cm in length.

#### Question 12:

Construct a rhombus the lengths of whose diagonals are 6 cm and 8 cm.

We know that the diagonals of a rhombus bisect each other.
.Steps of construction:
Step 1: Draw AC= $6cm$
Step 2:Draw a perpendicular bisector(XY) of AC, which bisects AC at O.
Step 3:

Draw an arc of length 4 cm on OX and name that point as B.
Draw an arc of length 4 cm on OY and name that point as D.
Step 4 : Join AB, BC, CD and AD.
​Thus, ABCD is the required rhombus, as shown in the figure.

#### Question 13:

Construct a rhombus ABCD in which AB = 4 cm and diagonal AC is 6.5 cm.

Steps of construction:
Step 1: Draw AB$4cm$
Step 2: With B as the centre, draw an arc of .
Step 3: With A as the centre, draw another arc of , cutting the previous arc at C.
​Step 4: Join AC and BC.
Step 5: With C as the centre, draw an arc of 4 cm.
Step 6: ​With A as the centre, draw another arc of , cutting the previous arc at D.
Step 7: Join AD and CD.
ABCD is the required rhombus.

#### Question 14:

Draw a rhombus whose side is 7.2 cm and one angle is 60°.

Steps of construction:
Step1: Draw AB
Step2: Draw
Sum of the adjacent angles is 180°.
$\angle BAX+\angle ABY=180°\phantom{\rule{0ex}{0ex}}=>\angle BAX=180°-60°=120°$
Step 3:

Step 4: Join C and D.
Then, ABCD is the required rhombus.

#### Question 15:

Construct a trapezium ABCD in which AB = 6 cm, BC = 4 cm, CD = 3.2 cm, ∠B = 75° and DC||AB.

Steps of construction:
Step 1: Draw AB=
Step 2: Make  $\angle ABX={75}^{\circ }$
Step 3: With B as the centre, draw an arc at $4cm$. Name that point as C.
Step 4:  $AB\parallel CD$

Make  $\angle BCY=105°$
At C, draw an arc of length .
Step 5: Join A and D.
Thus, ABCD is the required trapezium.

#### Question 16:

Draw a trapezium ABCD in which AB||DC, AB = 7 cm, BC = 5 cm, AD = 6.5 cm and ∠B = 60°.

Steps of construction :
Step1: Draw AB equal to 7 cm.
Step2: Make an angle,
Step3: With B as the centre, draw an arc of . Name that point as C. Join B and C.
Step4:

Draw an angle,

Step4: With A as the centre, draw an arc of length , which cuts CY. Mark that point as D.

Step5: Join A and D.

​Thus, ABCD is the required trapezium.

#### Question 1:

Define the terms:
(i) Open curve
(ii) Closed curve
(iii) Simple closed curve

( i) Open curve: An open curve is a curve where the beginning and end points are different.
Example:     Parabola

(ii) Closed Curve: A curve that joins up so there are no end points.
Example: Ellipse

(iii) Simple closed curve:  A closed curve that does not intersect itself.

#### Question 2:

The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find the measure of each angle.

Let the angles be
Sum of the angles of a quadrilateral is ${360}^{\circ }$.
$x+2x+3x+4x=360\phantom{\rule{0ex}{0ex}}10x=360\phantom{\rule{0ex}{0ex}}x=\frac{360}{10}\phantom{\rule{0ex}{0ex}}x=36$

$\left(2x\right)°=\left(2×36{\right)}^{\circ }={72}^{\circ }\phantom{\rule{0ex}{0ex}}\left(3x\right)°=\left(3×36{\right)}^{\circ }={108}^{\circ }\phantom{\rule{0ex}{0ex}}\left(4x\right)°=\left(4×36{\right)}^{\circ }={144}^{\circ }$

The angles of the quadrilateral are

#### Question 3:

Two adjacent angles of a parallelogram are in the ratio 2 : 3. Find the measure of each of its angles.

Sum of any two adjacent angles of a parallelogram is ${180}^{\circ }$.

$\left(2x\right)°=\left(2×36\right)°={72}^{\circ }\phantom{\rule{0ex}{0ex}}\left(3x\right)°=\left(3×36\right)°={108}^{\circ }$

Measures of the angles are .

#### Question 4:

The sides of a rectangle are in the ratio 4 : 5 and its perimeter is 180 cm. Find its sides.

Let the length be $4x$ cm and the breadth be $5x$ cm.
Perimeter of the rectangle =180 $cm$
Perimeter of the rectangle=$2\left(l+b\right)$

$2\left(l+b\right)=180\phantom{\rule{0ex}{0ex}}⇒2\left(4x+5x\right)=180\phantom{\rule{0ex}{0ex}}⇒2\left(9x\right)=180\phantom{\rule{0ex}{0ex}}⇒18x=180\phantom{\rule{0ex}{0ex}}⇒x=10$

#### Question 5:

Prove that the diagonals of a rhombus bisect each other at right angles.

Rhombus is a parallelogram.

Consider:

Therefore, the diagonals bisects at O.

Now, let us prove that the diagonals intersect each other at right angles.

Consider :

(corresponding parts of congruent triangles)

Further,

$\angle COD=\angle COB=90°$

It is proved that the diagonals of a rhombus are perpendicular bisectors of each other.

#### Question 6:

The diagonals of a rhombus are 16 cm and 12 cm. Find the length of each side of the rhombus.

All the sides of a rhombus are equal in length.
The diagonals of a rhombus intersect at ${90}^{\circ }$.
The diagonal and the side of a rhombus form right triangles.

In $△AOB$:

Therefore, the length of each side of the rhombus is 10 cm.

#### Question 7:

Mark (✓) against the correct answer:
Two opposite angles of a parallelogram are (3x − 2)° and (50 − x)°. The measures of all its angles are
(a) 97°, 83°, 97°, 83°
(b) 37°, 143°, 37°, 143°
(c) 76°, 104°, 76°, 104°
(d) none of these

(b) 37o, 143o, 37o 143o

Opposite angles of a parallelogram are equal.

Therefore, the first and the second angles are:
${\left(3x-2\right)}^{\circ }={\left(2×13-2\right)}^{\circ }={37}^{\circ }\phantom{\rule{0ex}{0ex}}{\left(50-x\right)}^{\circ }={\left(50-13\right)}^{\circ }={37}^{\circ }\phantom{\rule{0ex}{0ex}}$
Sum of adjacent angles in a parallelogram is ${180}^{\circ }$.
Adjacent angles = ${180}^{\circ }-{37}^{\circ }={143}^{\circ }$

#### Question 8:

Mark (✓) against the correct answer:
The angles of quadrilateral are in the ratio 1 : 3 : 7 : 9. The measure of the largest angle is
(a) 63°
(b) 72°
(c) 81°
(d) none of these

(d) none of the these

Let the angles be .

Sum of the angles of the quadrilateral is ${360}^{\circ }$.

$x+3x+7x+9x=360\phantom{\rule{0ex}{0ex}}20x=360\phantom{\rule{0ex}{0ex}}x=18$

#### Question 9:

Mark (✓) against the correct answer:
The length of a rectangle is 8 cm and each of its diagonals measures 10 cm. The breadth of the rectangle is
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) 9 cm

(b) 6 cm
Let the breadth of the rectangle be x cm.
Diagonal =10 cm
Length= 8 cm
The rectangle is divided into two right triangles.

Breadth of the rectangle = 6 cm

#### Question 10:

Mark (✓) against the correct answer:
In a square PQRS, if PQ = (2x + 3) cm and QR = (3x − 5) cm then
(a) x = 4
(b) x = 5
(c) x = 6
(d) x = 8

(d) x = 8
All sides of a square are equal.

#### Question 11:

Mark (✓) against the correct answer:
The bisectors of two adjacent angles of a parallelogram intersect at
(a) 30°
(b) 45°
(c) 60°
(d) 90°

(d) 90°

We know that the opposite sides and the angles in a parallelogram are equal.

Also, its adjacent sides are supplementary, i.e. sum of the sides is equal to 180.
Now, the bisectors of these angles form a triangle, whose two angles are:

Hence, the two bisectors intersect at right angles.

#### Question 12:

Mark (✓) against the correct answer:
How many diagonals are there in a hexagon?
(a) 6
(b) 8
(c) 9
(d) 10

(c) 9
Hexagon has six sides.

#### Question 13:

Mark (✓) against the correct answer:
Each interior angle of a polygon is 135. How many sides does it have?
(a) 10
(b) 8
(c) 6
(d) 5

(b) 8

It has 8 sides.

#### Question 14:

Fill in the blanks.
For a convex polygon of n sides, we have:
(i) Sum of all exterior angles = .........
(ii) Sum of all interior angles = .........
(iii) Number of diagonals = .........

(i) Sum of all exterior angles =  ${360}^{\circ }$

(ii) Sum of all interior angles = $\left(n-2\right)×180°\phantom{\rule{0ex}{0ex}}$

(iii) Number of diagonals = $\frac{n\left(n-3\right)}{2}$

#### Question 15:

Fill in the blanks.
For a regular polygon of n sides, we have:
(i) Sum of all exterior angles = .........
(ii) Sum of all interior angles = .........

(i) Sum of all exterior angles of a regular polygon is ${360}^{\circ }$.

(ii) Sum of all interior angles of a polygon is

#### Question 16:

Fill in the blanks.
(i) Each interior angle of a regular octagon is (.........)°.
(ii) The sum of all interior angles of a regular hexagon is (.........)°.
(iii) Each exterior angle of a regular polygon is 60°. This polygon is a .........
(iv) Each interior angle of a regular polygon is 108°. This polygon is a .........
(v) A pentagon has ......... diagonals.

(i) Octagon has 8 sides.

(ii) Sum of the interior angles of a regular hexagon = $\left(6-2\right)×{180}^{\circ }={720}^{\circ }$

(iii) Each exterior angle of a regular polygon is ${60}^{\circ }$.

Therefore, the given polygon is a hexagon.

(iv) If the interior angle is ${108}^{\circ }$, then the exterior angle will be ${72}^{\circ }$.                (interior and exterior angles are supplementary)
Sum of the exterior angles of a polygon is 360°.

Let there be n sides of a polygon.

$72n=360\phantom{\rule{0ex}{0ex}}n=\frac{360}{72}\phantom{\rule{0ex}{0ex}}n=5$

Since it has 5 sides, the polygon is a pentagon.

(v) A pentagon has 5 diagonals.

#### Question 17:

Write 'T' for true and 'F' for false for each of the following:
(i) The diagonals of a parallelogram are equal.
(ii) The diagonals of a rectangle are perpendicular to each other.
(iii) The diagonals of a rhombus bisect each other at right angles.
(iv) Every rhombus is a kite.

(i) F
The diagonals of a parallelogram need not be equal in length.

(ii) F
The diagonals of a rectangle are not perpendicular to each other.

(iii) T

(iv) T

Adjacent sides of a kite are equal and this is also true for a rhombus. Additionally, all the sides of a rhombus are equal to each other.

#### Question 18:

Construct a quadrilateral PQRS in which PQ = 4.2 cm, ∠PQR = 60°, ∠QPS = 120°, QR = 5 cm and PS = 6 cm.