# ICSE Class 8 Maths Selina Solutions for Chapter 16 Understanding Shapes

Chapter 16 Understanding shapes explains about properties of quadrilaterals, angle sum property, properties of parallelograms, kinds of quadrilaterals and theorems related to them. Knowing this chapter is important because it has applications in everyday life for eg: thinking about home projects, and in various careers, like architecture. For the better understanding of the concepts related to shapes, we have provided ICSE Class 8 maths Selina Solutions Chapter 16 – Understanding Shapes. These solutions are prepared by our subject experts. The questions are solved in the comprehensive way so that students can understand them easily.

Students of Class 8 ICSE can refer to the ICSE Class 8 maths Selina Solutions for Chapter 16 Understanding Shapes from the downloadable link provided below:

Chapter 16 of ICSE Class 8 Maths Selina Solutions is based on the topic Understanding Shapes. This chapter consists of a total of 15 questions in one exercise. All the solutions are solved in a proper step by step method for easy understanding of the students.

### CHAPTER 16 – UNDERSTANDING SHAPES

Exercise

Question 1.Â

Â State which of the following are polygons:Â

If the given figure is a polygon, name it as convex or concave.Â

Â Solution:Â

In given Fig. (ii), (iii) and (v) are polygons.

Fig. (ii) and (iii) are concave polygons while

Fig. (v) is convex.

QuestionÂ 2.Â

Calculate the sum of angles of a polygon with:Â

Â (i)Â 10Â sidesÂ

(ii)Â 12Â sidesÂ

Solution:-

No. of sidesÂ n=12

(iii)Â 20Â sidesÂ

Solution:-

n =20

(iv) 25 sidesÂ

Solution:-

n = 25

Question 3.Â

Find the number of sides in a polygon if the sum of its interior angles is:Â

Â (i)Â 900Â°

Solution:-

Let no. of sides = n

Sum of angles of polygon=Â 900Â°

(ii)Â 1620Â°

Solution:-

Let no. of sides = n

Sum of angles of polygon =Â 1620Â°

(iii)Â 16Â right-anglesÂ

Solution:-

Let no. of sidesÂ =n

Sum of angles of polygon =16

(iv)Â 32Â right-angles.Â

Solution:-

Let no. of sidesÂ =n

Sum of angles of polygonÂ =32

QuestionÂ 4.Â

Â Is it possible to have a polygon; whose sum of interior angles is?Â

Â (i)Â 870Â°

Solution:-

(i) Let no. of sides =Â n

Sum of anglesÂ =870Â°

Which is not a whole number.

Hence it is not possible to have a polygon, the sum of whose interior angles isÂ 870Â°

(ii)Â 2340Â°

Solution:

Let no. of sidesÂ =n

Sum of anglesÂ =2340Â°

Which is a whole number.

Hence it is possible to have a polygon, the sum of whose interior angles isÂ 2340Â°.

(iii)Â 7Â right-anglesÂ

Solution:-

Let no. of sidesÂ =n

Which is not a whole number. Hence it is not possible to have a polygon, the sum of whose interior angles isÂ 7Â right-angles.

Â (iv)Â 4500Â°

Solution:-

Let no. of sides =Â n

Which is a whole number.

Hence it is possible to have a polygon, the sum of whose interior angles isÂ 4500Â°.

QuestionÂ 5.

(i) If all the angles of a hexagon are equal; find the measure of each angle.

Solution:-

No. of sides of hexagon,Â n=6

Let each angle be =xÂ°

Sum of anglesÂ =6xÂ°

âˆ´Â Each angle of hexagonÂ =120Â°

(ii) If all the angles of aÂ 14Â â€“ sided figure are equal; find the measure of each angle.

Solution:-

No. of sides of polygon,Â n=14

Let each angleÂ =xÂ°

Sum of anglesÂ =14xÂ°

QuestionÂ 6.Â

FindÂ theÂ sumÂ ofÂ exteriorÂ anglesÂ obtainedÂ onÂ producing,Â inÂ order,Â theÂ sidesÂ ofÂ aÂ polygonÂ with:

(i)Â 7Â sides

(ii)Â 10Â sides

(iii)Â 250Â sides.

(i) Solution:

No.Â ofÂ sides n=7Â

SumÂ ofÂ interiorÂ exteriorÂ anglesÂ atÂ oneÂ vertexÂ =180Â°

=900Â°

âˆ´SumÂ ofÂ exteriorÂ anglesÂ =1260Â°-900Â°

=360Â°

(ii)Solution

No.Â ofÂ sidesÂ n=10

=1440Â°

âˆ´SumÂ ofÂ exteriorÂ anglesÂ  = 1800 â€“ 1440

SumÂ ofÂ exteriorÂ angles = 360Â°

(iii)Â  Solution:

No.Â ofÂ sideÂ n=250

SumÂ ofÂ allÂ interiorÂ andÂ exteriorÂ angles

=44640Â°

âˆ´ Sum of exterior angles =45000-44640

=360Â°

QuestionÂ 7Â :

TheÂ sidesÂ ofÂ aÂ hexagonÂ areÂ producedÂ inÂ order.Â IfÂ theÂ measuresÂ ofÂ exteriorÂ anglesÂ soÂ obtainedÂ are

(6x-1)Â° , (10Â x+2)Â°,(8Â x+2)Â°( 9Â x-3)Â°,(5Â x+4)Â° andÂ  (12Â x+6)Â°;Find each exterior angle.

Solution:-

SumÂ ofÂ exteriorÂ anglesÂ ofÂ hexagonÂ formedÂ byÂ producingÂ sidesÂ ofÂ orderÂ =360Â°

âˆ´(6x-1)Â°+(10x+2)Â°+(8x+2)Â°+(9x-3)Â° +(5x+4)Â°+(12x+6)Â°=360Â°

50x+10Â°=360Â°

50x=360Â°-10Â°

50x=350Â°

Â Question 8.Â

The interior angles of a pentagon are in the ratioÂ 4:5:6:7:5.Â Find each angle of the pentagon.

Solution:-

LetÂ theÂ interiorÂ anglesÂ ofÂ theÂ pentagonÂ beÂ 4Â x,Â 5Â x,Â 6Â x,Â 7Â x,Â 5Â x

TheirÂ sumÂ = 4Â x+5Â x+6Â x+7Â x+5Â x=27Â x

Question 9

TwoÂ anglesÂ ofÂ aÂ hexagonÂ areÂ 120Â°andÂ 160Â°.Â IfÂ theÂ remainingÂ fourÂ anglesÂ areÂ equal,Â find each equalÂ angle.

Solution:-

TwoÂ anglesÂ ofÂ aÂ hexagonÂ areÂ 120Â°,Â 160Â°

LetÂ remainingÂ fourÂ anglesÂ beÂ x,Â x,Â xÂ andÂ x.

TheirÂ sumÂ = 4Â x+280Â°

Question 10

TheÂ figure,Â givenÂ below,Â showsÂ aÂ pentagonÂ ABCDEÂ withÂ sidesÂ ABÂ andÂ EDÂ parallelÂ toÂ eachÂ other,Â and

<BÂ : <CÂ : <D:5:6:7.

(i) Using formula, find the sum of interior angles of the pentagon.

(ii) Write the value of âˆ A+âˆ E

(iii) Find angles B, C and D .

Solution:-

QuestionÂ 11.

Two angles of a polygon are right angles and the remaining areÂ 120Â°Â each. Find the number of sides in it.

Solution:-

Let number of sides = n

180Â n-540=120Â n-240

180Â n-120Â n=-240+540

60Â n=300

n = 300/60

n = 5

Question 12.

In a hexagon ABCDEF, side AB is parallel to side FE and âˆ B:âˆ C:âˆ D:âˆ E=6:4:2:3.find âˆ B and âˆ D.

Solution:-

Given: Hexagon ABCDEF in which AB II EF

andÂ âˆ B:âˆ C:âˆ D:âˆ E=6:4:2:3

To find :Â âˆ BÂ andÂ âˆ D

Proof:Â NoÂ of sidesÂ n=6

QuestionÂ 13.

the angles of a hexagon areÂ x+10Â°,2x+20Â°,2x-20Â°,3x-50Â°,x+40Â°Â andÂ x+20Â°.Â FindÂ x.

Solution:-

Angles of a hexagon areÂ x+10Â°, 2x+20Â°,

2x-20Â°, 3x-50Â°,x+40Â°Â andÂ x+20Â°

Â QuestionÂ 14.

In a pentagon, two angles areÂ 40Â°Â andÂ 60Â°Â and the rest are in the ratioÂ 1:3:7.Â Find the biggest angle of theÂ pentagon.

Solution:-

QuestionÂ 15

Â Fill in the blanks:Â

In case of regular polygon, with:

Solution:-

### ICSE Class 8 Maths Selina Solutions Chapter 16 – Understanding Shapes

The concepts discussed in Chapter 16 – Understanding Shapes will help students to solve the problems related to the topic by using different types of theorems explained in the chapter. The topic comes under the unit of Geometry and it is important from exam point of view. This topic helps in understanding the world around us through different patterns, areas, volumes, lengths and angles.

For all the other subjects like Physics, Chemistry and Biology students can get the answers by clicking on ICSE Class 8 Selina Solutions.

We hope that the information provided here for ICSE Class 8 Maths Selina Solutions Chapter 16 Understanding Shapes will help students while preparing for their Class 8 final exam.