ICSE Class 8 Maths Selina Solutions Chapter 16 Understanding Shapes

ICSE Class 8 Maths Selina Solutions Chapter 16 Overview

The solutions for ICSE Class 8 Maths Selina Solutions Chapter 16 "Understanding Shapes" are created by experts from Physics Wallah. It covers things like polygons (shapes with straight sides), how to classify them based on sides and angles, and how to find their perimeter and area. The solutions explain these ideas step by step with examples to help students understand them easily. They are designed to make learning geometry easier and to help students do well in exams by building a strong understanding of math concepts.

Understanding Shapes

ICSE Class 8 Maths Selina Solutions Chapter 16 Understanding Shapes PDF

You can find the PDF link for ICSE Class 8 Maths Selina Solutions Chapter 16 "Understanding Shapes" below. It is a useful resource for students looking to understand geometric shapes better and prepare effectively for exams.

ICSE Class 8 Maths Selina Solutions Chapter 16 Understanding Shapes PDF

ICSE Class 8 Maths Selina Solutions for Chapter 16 Understanding Shapes

Below we have provided ICSE Class 8 Maths Selina Solutions Chapter 16 Understanding Shapes for the ease of the students –

ICSE Class 8 Maths Selina Solutions for Chapter 16 Understanding Shapes Exercise 16 1

Question 1.

State which of the following are polygons:

If the (given figure in your book) is a polygon, name it as convex or concave.

Solution:

In given Fig. (ii), (iii) and (v) are polygons. Fig. (ii) and (iii) are concave polygons while Fig. (v) is convex.

Question 2.

Calculate the sum of angles of a polygon with:

(i) 10 sides

(ii) 12 sides

Solution:-

No. of sides n=12

(iii) 20 sides

Solution:-

n =20

(iv) 25 sides

Solution:-

n = 25

Question 3.

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

(i) 900°

Solution:-

Let no. of sides = n Sum of angles of polygon= 900°

(ii) 1620°

Solution:-

Let no. of sides = n Sum of angles of polygon = 1620°

(iii) 16 right-angles

Solution:-

Let no. of sides =n Sum of angles of polygon =16

(iv) 32 right-angles.

Solution:-

Let no. of sides =n Sum of angles of polygon =32

Question 4.

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

(i) 870°

Solution:-

(i) Let no. of sides = n Sum of angles =870° Which is not a whole number. Hence it is not possible to have a polygon, the sum of whose interior angles is 870°

(ii) 2340°

Solution:

Let no. of sides =n Sum of angles =2340° Which is a whole number. Hence it is possible to have a polygon, the sum of whose interior angles is 2340°.

(iii) 7 right-angles

Solution:-

Let no. of sides =n Which is not a whole number. Hence it is not possible to have a polygon, the sum of whose interior angles is 7 right-angles.

(iv) 4500°

Solution:-

Let no. of sides = n Which is a whole number. Hence it is possible to have a polygon, the sum of whose interior angles is 4500°.

Question 5.

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

Solution:-

No. of sides of hexagon, n=6 Let each angle be =x° Sum of angles =6x° ∴ Each angle of hexagon =120° (ii) If all the angles of a 14 – sided figure are equal; find the measure of each angle.

Solution:-

No. of sides of polygon, n=14 Let each angle =x° Sum of angles =14x°

Question 6.

Find the sum of exterior angles obtained on producing, in order, the sides of a polygon with: (i) 7 sides (ii) 10 sides (iii) 250 sides.

(i) Solution:

No. of sides n=7

Sum of interior exterior angles at one vertex =180° =900° ∴Sum of exterior angles =1260°-900° =360°

(ii)Solution

No. of sides n=10

=1440° ∴Sum of exterior angles  = 1800 – 1440 Sum of exterior angles = 360°

(iii)  Solution:

No. of side n=250

Sum of all interior and exterior angles =44640° ∴ Sum of exterior angles =45000-44640 =360°

Question 7 :

The sides of a hexagon are produced in order. If the measures of exterior angles so obtained are

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

Solution:-

Sum of exterior angles of hexagon formed by producing sides of order =360° ∴(6x-1)°+(10x+2)°+(8x+2)°+(9x-3)° +(5x+4)°+(12x+6)°=360° 50x+10°=360° 50x=360°-10° 50x=350°

Question 8.

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

Solution:-

Let the interior angles of the pentagon be 4 x, 5 x, 6 x, 7 x, 5 x Their sum = 4 x+5 x+6 x+7 x+5 x=27 x

Question 9

Two angles of a hexagon are 120°and 160°. If the remaining four angles are equal, find each equal angle.

Solution:-

Two angles of a hexagon are 120°, 160° Let remaining four angles be x, x, x and x. Their sum = 4 x+280°

Question 10

The figure, given below, shows a pentagon ABCDE with sides AB and ED parallel to each other, and <B : <C : <D:5:6:7. (i) Using formula, find the sum of interior angles of the pentagon. (ii) Write the value of ∠A+∠E (iii) Find angles B, C and D .

Solution:-

Question 11.

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

Solution:-

Let number of sides = n 180 n-540=120 n-240 180 n-120 n=-240+540 60 n=300 n = 300/60 n = 5

Question 12.

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

Solution:-

Given: Hexagon ABCDEF in which AB II EF and ∠B:∠C:∠D:∠E=6:4:2:3 To find : ∠B and ∠D Proof: No of sides n=6

Question 13.

the angles of a hexagon are x+10°,2x+20°,2x-20°,3x-50°,x+40° and x+20°. Find x.

Solution:-

Angles of a hexagon are x+10°, 2x+20°, 2x-20°, 3x-50°,x+40° and x+20°

Question 14.

In a pentagon, two angles are 40° and 60° and the rest are in the ratio 1:3:7. Find the biggest angle of the pentagon.

Solution:-

Question 15

Fill in the blanks:

In case of regular polygon, with:

Solution:-

Benefits of ICSE Class 8 Maths Selina Solutions for Chapter 16 Understanding Shapes

Clarity and Explanation : These Solutions provide clear explanations of geometric concepts, making it easier for students to understand shapes and their properties.

Step-by-Step Guidance : They provide step-by-step solutions that help students navigate through the calculations of perimeter, area, and other geometric measurements.

Illustrative Examples : Solutions include practical examples that illustrate how to classify polygons and understand symmetry, aiding better comprehension.

Preparation for Exams : By using these solutions students can effectively prepare for exams by practicing and mastering key geometric principles.

Enhanced Problem-Solving Skills : They help in developing problem-solving skills by applying mathematical formulas and concepts to solve geometry-related problems.

Builds Confidence : Detailed solutions build confidence among students as they gain proficiency in handling geometric shapes and their applications.