Class 8 Maths Notes for Understanding Quadrilaterals
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Page 1
NOTES
CLASS 8
MATHS
Study Material
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CLASS 8
MATHS
Study Material
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Page 2
UNDERSTANDING QUADRANGLES
IMPORTANT CONCEPTS
Polygon – polygon is a simple closed curve formed an only live segment.
Convex and concave polygons – a polygon is said to be convex if it has no portion of its diagonal in its
exterior otherwise it is a triangular polygon.
Regular and irregular polygons – a polygon which is both, all angles and all sides are equal is called regular
polygon otherwise it is irregular polygon.
Special name of polygon according to its sides (3 side, triangle) (4 sides, quadrilateral) (5 sides, pentagon) ,
(6 sides, hexagon)
Sum of exterior angle angles of polygon is always 360𝑜 .
36 0°
Exterior angle of polygon = 𝑛
360 °
Number of sides of regular polygon = 𝑜𝑛𝑒𝑒𝑥𝑡𝑒𝑟𝑖
𝑜𝑟𝑎𝑛𝑔𝑙𝑒
(𝑛−2)180 °
Interior angle of regular polygon 𝑛
Def. of triangles, Types of triangles.
Sum of interior angles of interior angles of triangles of its 180 °
Def. of quadrilateral, types of quadrilaterals and its properties
Sum of interior angles of quadrilateral is 360 °
Examples with solutions:
1. What is the name of regular polygon with 4 sides?
a. Equilateral triangle b. square c. rectangle d. kite
2. How many sides a regular polygon will have if its exterior angles are of 45°?
a. 4 b. 6 c. 3 d. 5
3. What is the name of regular polygon of 6 sides?
a. Square b. pentagon c. hexagon d. octagon
4. How many diagonals does a quadrilateral have?
a. 1 b. 2 c. 3 d. 4
ANSWER:Q1 (b) Q2 (c) Q3 (c) Q4 (b)
Case Study Based Questions
1. Identify polygon in red colour?
2. What is the measure of each interior angle of the polygon?
3. What is the measure of each exterior angle of the polygon
Answer Case Study Based Question: 1) Hexagon 2) 1200 3) 600
Short Answer Type Questions
1. How many sides does a regular polygon have if each its interior angle is
165°?
2. What is the minimum interior angle possible in a regular polygon?
3. How many sides does a regular polygon have if the measure of its exterior angle is 36°?
Short Answer Question: Q1 24sides Q2 600 Q3 10 Sides
Long Answer Type Questions
1. ABCD is a parallelogram. Find the angle if x, y and z.
12
IMPORTANT CONCEPTS
Polygon – polygon is a simple closed curve formed an only live segment.
Convex and concave polygons – a polygon is said to be convex if it has no portion of its diagonal in its
exterior otherwise it is a triangular polygon.
Regular and irregular polygons – a polygon which is both, all angles and all sides are equal is called regular
polygon otherwise it is irregular polygon.
Special name of polygon according to its sides (3 side, triangle) (4 sides, quadrilateral) (5 sides, pentagon) ,
(6 sides, hexagon)
Sum of exterior angle angles of polygon is always 360𝑜 .
36 0°
Exterior angle of polygon = 𝑛
360 °
Number of sides of regular polygon = 𝑜𝑛𝑒𝑒𝑥𝑡𝑒𝑟𝑖
𝑜𝑟𝑎𝑛𝑔𝑙𝑒
(𝑛−2)180 °
Interior angle of regular polygon 𝑛
Def. of triangles, Types of triangles.
Sum of interior angles of interior angles of triangles of its 180 °
Def. of quadrilateral, types of quadrilaterals and its properties
Sum of interior angles of quadrilateral is 360 °
Examples with solutions:
1. What is the name of regular polygon with 4 sides?
a. Equilateral triangle b. square c. rectangle d. kite
2. How many sides a regular polygon will have if its exterior angles are of 45°?
a. 4 b. 6 c. 3 d. 5
3. What is the name of regular polygon of 6 sides?
a. Square b. pentagon c. hexagon d. octagon
4. How many diagonals does a quadrilateral have?
a. 1 b. 2 c. 3 d. 4
ANSWER:Q1 (b) Q2 (c) Q3 (c) Q4 (b)
Case Study Based Questions
1. Identify polygon in red colour?
2. What is the measure of each interior angle of the polygon?
3. What is the measure of each exterior angle of the polygon
Answer Case Study Based Question: 1) Hexagon 2) 1200 3) 600
Short Answer Type Questions
1. How many sides does a regular polygon have if each its interior angle is
165°?
2. What is the minimum interior angle possible in a regular polygon?
3. How many sides does a regular polygon have if the measure of its exterior angle is 36°?
Short Answer Question: Q1 24sides Q2 600 Q3 10 Sides
Long Answer Type Questions
1. ABCD is a parallelogram. Find the angle if x, y and z.
12
Page 3
2. In a parallelogram PQRS find the value of x and y.
Answer Long Answer Type Questions:
Q1 𝑥 = 1100 , 𝑦 = 300 𝑧 = 400 Q2 𝑥 = 11 , 𝑦 = 5
PRACTICE QUESTIONS:
MCQs
1. In a parallelogram opposite angles are?
a. Equal b. half c. doubled. d. none of these
2. In a rectangle all angles are?
a. 45 ° b. 90 ° c. 100 ° d. 180 °
3. In a square both the diagonals are?
a. Equal b. unequal c. sometimes equal, sometimes unequal d. none of these
4. How many diagonals does a pentagon have?
a. 4 b. 5 c. 6 d. 7
5. What is the name of regular polygon of 4 sides?
a. Equilateral triangle b. square c. rectangle d. kite
6. The measure of exterior angle of a regular polygon of 9 sides is?
a. 30 ° b. 40 ° c. 50 ° d. 60 °
7. The sum of measure of exterior angle of any polygon is?
a. 90 ° b. 180 ° c. 720 ° d. 360 °
8. How many sides does a regular polygon have if its interior angle is 150°?
a. 8 b. 10 c. 12 d. 14
9. What is the name of a regular polygon of 10 sides?
a. Hexagon b. octagon c. decagon d. none of these.
10. How many vertices does a quadrilateral have?
a. 4 b. 3 c. 5 d. 6
Short Answer Types Questions
1. What is a regular polygon, State the name of regular polygon of 5 sides.
2. Find the sum of interior angle of a pentagon.
3. Is it possible to have a regular polygon with measure of each exterior angle 25 °?
4. Is rhombus a square?
5. Is rectangle a parallelogram?
6. How many sides does a regular polygon have if each of the interior angle is 165 °?
7. In a parallelogram one angle is 70 °. Find all the other angles of the parallelogram?
8. The four angles of a Quadrilateral are in the ratio 1:2:3:4 find the measure of smaller and greater
angle.
9. ABCD find the value of x and y
10. In a parallelogram PQRS, ∠𝑃 ∶ ∠𝑄 = 1: 2 Then find ∠𝑄 = ?
Long Answer Type Question
1. In a parallelogram two adjacent angles are in the same ratio 4:5 find each angle of the parallelogram?
13
Answer Long Answer Type Questions:
Q1 𝑥 = 1100 , 𝑦 = 300 𝑧 = 400 Q2 𝑥 = 11 , 𝑦 = 5
PRACTICE QUESTIONS:
MCQs
1. In a parallelogram opposite angles are?
a. Equal b. half c. doubled. d. none of these
2. In a rectangle all angles are?
a. 45 ° b. 90 ° c. 100 ° d. 180 °
3. In a square both the diagonals are?
a. Equal b. unequal c. sometimes equal, sometimes unequal d. none of these
4. How many diagonals does a pentagon have?
a. 4 b. 5 c. 6 d. 7
5. What is the name of regular polygon of 4 sides?
a. Equilateral triangle b. square c. rectangle d. kite
6. The measure of exterior angle of a regular polygon of 9 sides is?
a. 30 ° b. 40 ° c. 50 ° d. 60 °
7. The sum of measure of exterior angle of any polygon is?
a. 90 ° b. 180 ° c. 720 ° d. 360 °
8. How many sides does a regular polygon have if its interior angle is 150°?
a. 8 b. 10 c. 12 d. 14
9. What is the name of a regular polygon of 10 sides?
a. Hexagon b. octagon c. decagon d. none of these.
10. How many vertices does a quadrilateral have?
a. 4 b. 3 c. 5 d. 6
Short Answer Types Questions
1. What is a regular polygon, State the name of regular polygon of 5 sides.
2. Find the sum of interior angle of a pentagon.
3. Is it possible to have a regular polygon with measure of each exterior angle 25 °?
4. Is rhombus a square?
5. Is rectangle a parallelogram?
6. How many sides does a regular polygon have if each of the interior angle is 165 °?
7. In a parallelogram one angle is 70 °. Find all the other angles of the parallelogram?
8. The four angles of a Quadrilateral are in the ratio 1:2:3:4 find the measure of smaller and greater
angle.
9. ABCD find the value of x and y
10. In a parallelogram PQRS, ∠𝑃 ∶ ∠𝑄 = 1: 2 Then find ∠𝑄 = ?
Long Answer Type Question
1. In a parallelogram two adjacent angles are in the same ratio 4:5 find each angle of the parallelogram?
13
Page 4
2. Perimeter of rectangle is 120 cm. if their length and width are in the ratio 2:3. Find the length and
breadth of the diagonals.
3. If two diagonal of a parallelogram are 𝑥 + 𝑦 = 8 𝑎𝑛𝑑𝑥 − 𝑦 = 2 find the length the diagonals.
4. The angles of a quadrilateral and its ratio its ratio 2: 3: 4: 6 .
Find its all angles.
5. In a parallelogram ABCD. Find the value of x, y and z. name the
type of triangle ABC.
6. ABCD is a rhombus find the value of x y and z.
Case Study Based Question
1. Take a regular hexagon and answer the following questions:
a. What is the sum of measure of its exterior angles a, b, c, d, e, and
f?
b. Is 𝑎 = 𝑏 = 𝑐 = 𝑑 = 𝑒 = 𝑓 ? why?
c. What is the measure of each exterior angle and interior
angle?
ANSWER
MCQS
Q1 (a) Q2 (b) Q3 (a) Q4 (5) Q5 (b) Q6 (b) Q7 (d)
Q8 (c) Q9 (C) Q10 (a)
SHORT ANSWER TYPE QUESTION
Q1: All sides are equal, Pentagon Q2: 5400 Q3: NO Q4: NO Q5: YES
0 0 0 0 0 0
Q6: 24 Q7: 70 ,110 ,70 ,110 Q8: 𝑥 = 5 , 𝑦 = 11 Q9: 360 , 144 Q10 <Q = 1200
LONG ANSWER TYPE QUESTION
Q1 800 , 1000 Q2 L = 24cm B = 36 cm Q3 x = 5, y = 3 Q4 480 ,720 ,960 ,1440
Q5 x = 1200 ,y = 300 ,z = 300 Q6 x = 500 ,y = 500 , z = 900
0
CASE STUDY BASE QUESTION: (i) 360 (ii) Yes polygon is regular (iii) 600
14
breadth of the diagonals.
3. If two diagonal of a parallelogram are 𝑥 + 𝑦 = 8 𝑎𝑛𝑑𝑥 − 𝑦 = 2 find the length the diagonals.
4. The angles of a quadrilateral and its ratio its ratio 2: 3: 4: 6 .
Find its all angles.
5. In a parallelogram ABCD. Find the value of x, y and z. name the
type of triangle ABC.
6. ABCD is a rhombus find the value of x y and z.
Case Study Based Question
1. Take a regular hexagon and answer the following questions:
a. What is the sum of measure of its exterior angles a, b, c, d, e, and
f?
b. Is 𝑎 = 𝑏 = 𝑐 = 𝑑 = 𝑒 = 𝑓 ? why?
c. What is the measure of each exterior angle and interior
angle?
ANSWER
MCQS
Q1 (a) Q2 (b) Q3 (a) Q4 (5) Q5 (b) Q6 (b) Q7 (d)
Q8 (c) Q9 (C) Q10 (a)
SHORT ANSWER TYPE QUESTION
Q1: All sides are equal, Pentagon Q2: 5400 Q3: NO Q4: NO Q5: YES
0 0 0 0 0 0
Q6: 24 Q7: 70 ,110 ,70 ,110 Q8: 𝑥 = 5 , 𝑦 = 11 Q9: 360 , 144 Q10 <Q = 1200
LONG ANSWER TYPE QUESTION
Q1 800 , 1000 Q2 L = 24cm B = 36 cm Q3 x = 5, y = 3 Q4 480 ,720 ,960 ,1440
Q5 x = 1200 ,y = 300 ,z = 300 Q6 x = 500 ,y = 500 , z = 900
0
CASE STUDY BASE QUESTION: (i) 360 (ii) Yes polygon is regular (iii) 600
14
Page 5
TEST-1 (20 MARKS)
SECTION A (2 marks each)
1. What is the name of regular polygon of 6 sides?
2. In a parallelogram opposite angles are?
3. In a rectangle all angles are?
4. In a square both the diagonals are?
5. How many diagonals does a pentagon have?
6. What is the name of regular polygon of 4 sides?
SECTION B (4 marks each)
7. In a parallelogram two adjacent angles are in the same ratio 4:5 find each angle of the parallelogram?
8. Perimeter of rectangle is 120 cm. if their length and width are in the ratio 2:3. Find the length and
breadth of the rectangle.
TEST-2 (30 MARKS)
SECTION A (2 marks each)
1. The sum of measure of exterior angle of any polygon is?
2. How many sides does a regular polygon have if its interior angle is 150°?
3. What is the name of a regular polygon of 10 sides.
SECTION B (3 marks each)
4. How many sides does a regular polygon have if each of the interior angle is 165 °?
5. In a parallelogram one angle is 70 °. Find all the other angles of the parallelogram?
6. Two diagonals of a parallelogram are x + y = 8 and x - y = 2 find the lengths of the diagonals.
7. The angles of a quadrilateral and its ratio its ratio 2:3:4:6 find its all angles.
SECTION C (4 marks each)
8. The four angles of Quadrilateral are in the ratio 1:2:3:4 find the
measure of smaller and greater angle.
9. ABCD find the value of x and y.
10. In a parallelogram PQRS, ∠𝑃 ∶ ∠𝑄 = 1: 2 Then find
15
SECTION A (2 marks each)
1. What is the name of regular polygon of 6 sides?
2. In a parallelogram opposite angles are?
3. In a rectangle all angles are?
4. In a square both the diagonals are?
5. How many diagonals does a pentagon have?
6. What is the name of regular polygon of 4 sides?
SECTION B (4 marks each)
7. In a parallelogram two adjacent angles are in the same ratio 4:5 find each angle of the parallelogram?
8. Perimeter of rectangle is 120 cm. if their length and width are in the ratio 2:3. Find the length and
breadth of the rectangle.
TEST-2 (30 MARKS)
SECTION A (2 marks each)
1. The sum of measure of exterior angle of any polygon is?
2. How many sides does a regular polygon have if its interior angle is 150°?
3. What is the name of a regular polygon of 10 sides.
SECTION B (3 marks each)
4. How many sides does a regular polygon have if each of the interior angle is 165 °?
5. In a parallelogram one angle is 70 °. Find all the other angles of the parallelogram?
6. Two diagonals of a parallelogram are x + y = 8 and x - y = 2 find the lengths of the diagonals.
7. The angles of a quadrilateral and its ratio its ratio 2:3:4:6 find its all angles.
SECTION C (4 marks each)
8. The four angles of Quadrilateral are in the ratio 1:2:3:4 find the
measure of smaller and greater angle.
9. ABCD find the value of x and y.
10. In a parallelogram PQRS, ∠𝑃 ∶ ∠𝑄 = 1: 2 Then find
15
Page 6
Study Materials
Notes
Model Papers Class 6 Notes
Sample Papers Class 7 Notes
Half Yearly Sample Papers Class 8 Notes
Class 9 Notes
Important Resources
Class 10 Notes
Periodic Table
Class 11 Notes
Writing Skills / Formats
Maps of India / World Class 12 Notes
Books and Solutions
NCERT Books
NCERT Book Solutions
HC Verma Chapter Wise Solutions
RD Sharma Solutions
CGBSE Solutions
Notes
Model Papers Class 6 Notes
Sample Papers Class 7 Notes
Half Yearly Sample Papers Class 8 Notes
Class 9 Notes
Important Resources
Class 10 Notes
Periodic Table
Class 11 Notes
Writing Skills / Formats
Maps of India / World Class 12 Notes
Books and Solutions
NCERT Books
NCERT Book Solutions
HC Verma Chapter Wise Solutions
RD Sharma Solutions
CGBSE Solutions
Document Details
| Board / Org | Aglasem |
| Exam | Class 8 |
| Type | Notes |
| Pages | 6 |
| Language | english |
| Updated | 30 Apr 2026 |