Polygon Class-6 RS Aggarwal ICSE Maths Goyal Brothers Prakashan

Polygon Class-6 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions Chapter-19 Solutions. We provide step by step Solutions of Exercise / lesson-19 Polygon for ICSE Class-6 RS Aggarwal Mathematics.

Our Solutions contain all type Questions with Exe-19 with Notes on Polygon to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-6  Maths.

Polygon Class-6 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions Chapter-19 Solutions

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Notes on Polygon

Exe-19

Notes on Polygon

A polygon is a closed figure bounded by three or more line segments that intersect exactly to form a closed curve.

Basic Terms in Polygons

• Sides: The line segments that forms a polygon is termed as sides. From the above polygon, we can say that line segment AB, BC, CD, DA are four sides of the polygon.
• Vertex: The meeting of two sides is termed as vertex. From the above polygon, we can say that A is a vertex as DA and AB meets at A. Similarly, B, C and D are also vertices of the polygon.
• Adjacent Sides: In a polygon, any two sides that has a common end are termed as adjacent sides. From the above polygon, we can say that sides CD and BC are adjacent as they terminate at a common end C. Similarly, sides AB and DA, AB and BC, CD and DA are also adjacent.
• Adjacent Vertices: End points of the same side of the polygon are termed as adjacent vertex. From the above polygon, we can say that C and D are adjacent vertices while A and C are not adjacent vertices.
• Diagonals: The line joining the non-adjacent vertices of a polygon is termed as diagonals. From the above polygon, we can say that line segment AC and DB are the diagonals of the polygon.

 classification of polygons

Regular Polygon

In a regular polygon, all the sides of the polygon are equal, and all the interior angles are the same.

Irregular Polygon

A polygon with an irregular shape. It means the sides and angles of the polygon are not equal.

Convex Polygon

In a convex polygon, the measure of the interior angle is less than 180 degrees

Concave Polygon

In a concave polygon, at least one angle measures more than 180 degrees. The vertices of a concave polygon are inwards as well as outwards

Important for Polygon

Exterior angle + Adjacent Angle = 180°

Sum of the All interior angles of n side polygon = (2n-4) x 90

Exe-19

Polygon Class-6 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions Chapter-19 Solutions

Page 233-234

Question 1:

Which of the following are simple closed figures ?

Answer :

Figures (i), (ii) and (iv) are simple closed figures.

Question 2:

Which of the following figures are polygons ? Name them, if any.

Answer :

(i) No.

(ii) Yes, this is concave quadrilateral.

(iii) Yes, concave hexagon.

(iv) Yes, regular hexagon.

(v) Yes, concave decagon.

(vi) Yes, concave 12-gon.

Question 3:

Find the sum of the interior angles of a :

(i) nonagon

(ii) 16-sided polygon

Answer :

(i) A nonagon has 9 sides

so, sum of interior angles of nonagon

= (2 x 9 – 4) right angle

= 14 x 90°  = 1260°

(ii) Sum of interior angles of a 16 sided polygon

= (2 x 16 – 4) right angle.

= 28 x 90°   = 2520°

Question 4:

Find the measure of each interior angle of a :

(i) regular decagon

(ii) regular 18-sided polygon

Answer :

(i) A decagon has 10 sides
Sum of interior angles of a decagon
= (2 x 10 – 4) right angles
16 x 90°  = 1440°

Since, the interior angles of a regular polygon are of the same measures,

so we have each interior angle of (1440°/10)
= 144° regular decagon

(ii) Sum of interior angle of a regular 18-sided polygon

= (2 x 18 – 4) x 90° = 2880°
Since, the interior angles of a regular polygon are of the same measure,

so we have each interior angle of (2880/18) =  160° g

Question 5:

Five of the angles of a hexagon are each 115°. Calculate the measure of the sixth angle.

Answer :

A hexagon has 6 sides
Sum of interior angles of a hexagon

= (2 x 6 – 4) right angles

= 8 x 90°

= 720°
Sixth angle= 720° – (115° + 115° + 115 + 115° + 115°)

= 720° – 575°
= 145°

Question 6:

The angles of a heptagon are (x + 3)°,  (2x + 5)°. Cr+8)°,  (3x + 1)°, (5x – 6)°, (2x + 9)° and (x -5)°. Calculate x.
Answer :

In a heptagon, n =7
So, Sum of its interior angles
= (2 – 4) right angles
= (2 x 7 – 4) x 90°
(14 – 4) x 90°
10 x 90° = 900°

But sum of its angles are :
(x + 3)° + (2x + 5)° + (x + 8)° + (3x + 1)° + (5x – 6)° + (2x + 9)° + (x – 5)°
= X + 3 + 2x + 5 + X + 8 + 3x + 1 + 5x -6 + 2x + 9 + x – 5
= 15x + 26 – 11  = 15 x+ 15°
= 15x = 900° – 15° 885°
= x = (885°/15°) = 59°
Hence,

x = 59°

Question 7:

An octagon has three equal angles each of measure 11S°. If all the remaining angles have equal measure, find the measure of each of these remaining angle.

Answer :
Sum of angles of an octagon (n = 8)
= (2n – 4) angles
=(2 x 8 – 4) x 90° = (16-4) x 90°
12 x 90° = 1080°

Sum of three angles of it = 115° x 3 = 345°
So, Sum of remaining 5 angles 1080° – 345° = 735°
So, Measure of each angle = (735°/5) = 147°

Question 8:

The sum of the interior angles of a polygon is 2160°. How many sides does this polygon have ?

Answer :
The number of sides of the polygon be n.

Then, sum of interior angles of the polygon
=  (2n – 4) right angles
=  (2n – 4) x 90°
So, (2n – 4) x 90° = 2160°
= (2n – 4) = 2160/90
= 24
= 2n = 28
= n = 14

n = (360/18) = 20

Hence, the polygon has 20 sides.

(iii)

n = (360/30) = 12

Hence, the polygon has 12 sides.

Question 10:

Find the measure of each exterior angle of a regular decagon.

Answer :

Each interior angle = [(2 x 10 – 4) x 90°/10]

= 144°

Each exterior angle = 180° – Each interior angle = 180° – 144°

 = 36°

So, Each exterior angle of a regular decagon = 36°

–: End of Polygon Class-6 RS Aggarwal Solutions :–

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