NCERT Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.1


Chapter 3 Understanding Quadrilaterals Exercise 3.1

Question 1: Given here are some figures.
Classify each of them on the basis of the following.
a) Simple curve
b) Simple closed curve
c) Polygon
d) Convex polygon
e) Concave polygon
Answer:

a) Simple curve: 1, 2, 5, 6 and 7
b) Simple closed curve: 1, 2, 5, 6 and 7
c) Polygon: 1 and 2
d) Convex polygon: 2
e) Concave polygon: 1

Question 2: How many diagonals does each of the following have?
a) A convex quadrilateral
b) A regular hexagon
c) A triangle
Answer:
a)
Number of sides a convex quadrilateral has = 4
Formula for finding diagonal = n × (n - 3)
= 4 × (4 - 3)/2
= 4 × 1/2
= 4/2
= 2 diagonals

b)
Number of sides a regular hexagon has = 6
Formula for finding diagonal = n × (n - 3)
= 6 × (6 - 3)/2
= 6 × 3/2
= 18/2
= 9 diagonals

c)
Number of sides a triangle has = 3
Formula for finding diagonal = n × (n - 3)
= 3 × (3 - 3)/2
= 3 × 0/2
= 0/2
= 0 diagonals

Question 3: What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)
Answer:
The sum of measures of the angles of a convex quadrilateral is 360°. Yes, this property will hold if the quadrilateral is not convex.
Sum of all angles in a triangle = 180°
= △ABC + △ACD = ?
= 180° + 180° = 360°

Question 4: Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)
What can you say about the angle sum of a convex polygon with number of sides?
a) 7
b) 8
c) 10
d) n
Answer:

a)
Number of sides = 7
Formula for finding angle sum property = (n - 2) × 180°
= (7 - 2) × 180°
= 5 × 180°
= 900°

b)
Number of sides = 8
Formula for finding angle sum property = (n - 2) × 180°
= (8 - 2) × 180°
= 6 × 180°
= 1080°

c)
Number of sides = 10
Formula for finding angle sum property = (n - 2) × 180°
= (10 - 2) × 180°
= 8 × 180°
= 1440°

d)
Number of sides = n
Formula for finding angle sum property = (n - 2) × 180°
= (n - 2) × 180°
= (n - 2) × 180°

Question 5: What is a regular polygon?
State the name of a regular polygon of
i) 3 sides
ii) 4 sides
iii) 6 sides
Answer:

Polygons which are equiangular and equilateral are called regular polygon.
i) A regular polygon of 3 sides is equilateral triangle.
ii) A regular polygon of 4 sides is square.
iii) A regular polygon of 6 sides is regular hexagon.

Question 6: Find the angle measure x in the following figures.
Answer:

a) Angle sum property of quadrilateral = 360°
= ∠50° + ∠130° + ∠120° + ∠x = 360°
= 300° + x = 360°
= x = 360 - 300
= x = 60°

b) Angle sum property of quadrilateral = 360°
= ∠60° + ∠70° + ∠x + ∠90° = 360°
= 220° + x = 360°
= x = 360 - 220
= x = 140°

c) Angle sum property of pentagon = 540°
= ∠30° + ∠110° + ∠120° + ∠x + ∠x = 540°
= 260° + 2x = 540°
= 2x = 540 - 260
= 2x = 280
= x = 280/2
= x = 140°

d) Angle sum property of regular pentagon = 540°
= ∠x + ∠x + ∠x + ∠x + ∠x = 540°
= 5x = 540°
= x = 540/5
= x = 108°

Question 7:
Answer:

a)
Angle sum property of triangle = 180°
= ∠30° + ∠90° + ∠a = 180°
= 120° + a = 180°
= a = 180 - 120
= a = 60°
Therefore,
z = 180° - 30° = 150° (supplementary angles equal to 180°)
x = 180° - 90° = 90° (supplementary angles equal to 180°)
y = 180° - 60° = 120° (supplementary angles equal to 180°)

b)
Angle sum property of quadrilateral = 360°
= ∠120° + ∠80° + ∠60°+ ∠a = 360°
= 260° + a = 360°
= a = 360 - 260
= a = 100°
Therefore,
w = 180° - 100° = 30° (supplementary angles equal to 180°)
x = 180° - 120° = 60° (supplementary angles equal to 180°)
y = 180° - 80° = 100° (supplementary angles equal to 180°)
z = 180° - 60° = 120° (supplementary angles equal to 180°)

No comments:

Post a Comment

Also read!

Click on any of the below text for additional links:

Class 6

Class 6 Computer Kips Solutions
Class 6 Gul Mohar English Solutions
→ Class 6 Map Pointing Solutions
Class 6 NCERT Civics Solutions
Class 6 NCERT Geography Solutions
Class 6 NCERT History Solutions
Class 6 NCERT Maths Solutions
Class 6 NCERT Science Solutions

Class 7

Class 7 Computer Kips Solutions
Class 7 Gul Mohar English Solutions
English Grammar Class 7
English Writing Skills Class 7
Class 7 Map Pointing Solutions
Class 7 NCERT Civics Solutions
Class 7 NCERT Civics Notes
Class 7 NCERT Civics Extra Questions
Class 7 NCERT Geography Solutions
Class 7 NCERT Geography Notes
Class 7 NCERT Geography Extra Questions
Class 7 NCERT History Solutions
Class 7 NCERT History Notes
Class 7 NCERT History Extra Questions
Class 7 NCERT Maths Solutions
Class 7 NCERT Science Solutions
Class 7 NCERT Science Notes
Class 7 NCERT Science Extra Questions

Class 8

Class 8 Kips Artificial Intelligence Solutions
Class 8 Gul Mohar English Solutions
English Grammar Class 8
English Writing Skills Class 8
Class 8 Map Pointing Solutions
Class 8 NCERT Civics Solutions
Class 8 NCERT Civics Notes
Class 8 NCERT Civics Extra Questions
Class 8 NCERT Geography Solutions
Class 8 NCERT Geography Notes
Class 8 NCERT Geography Extra Questions
Class 8 NCERT History Solutions
Class 8 NCERT History Notes
Class 8 NCERT History Extra Questions
Class 8 NCERT Maths Solutions
Class 8 NCERT Science Solutions
Class 8 NCERT Science Notes
Class 8 NCERT Science Extra Questions
Class 8 NCERT Science Exemplar
Class 8 NCERT Science MCQs

Class 9

Class 9 Kips Artificial Intelligence Solutions
Class 9 Map Pointing Solutions
Class 9 NCERT Civics Solutions
Class 9 NCERT Geography Solutions
Class 9 NCERT History Solutions
Class 9 NCERT Maths Solutions
Class 9 NCERT Science Solutions

Class 10

Class 10 Kips Artificial Intelligence Solutions
Class 10 NCERT English Solutions
→ Class 10 Map Pointing Solutions
Class 10 NCERT Civics Solutions
Class 10 NCERT Civics Notes
Class 10 NCERT Civics Extra Questions
Class 10 NCERT Geography Solutions
Class 10 NCERT Geography Notes
Class 10 NCERT Geography Extra Questions
Class 10 NCERT History Solutions
→ Class 10 NCERT History Notes
Class 10 NCERT History Extra Questions
Class 10 NCERT Maths Solutions
Class 10 NCERT Science Solutions
Class 10 NCERT Science Notes
Class 10 NCERT Science Extra Questions

Computer Languages

Python Basics

Extra Activities

Extra Activities

Extra Knowledge

Extra Information
General Knowledge
Historical Places in India
Latest technology
Physical Sciences
Facts

• Mathematics quick links
Mathematical Terms
Maths Tricks

Home Top