Chapter 6 - Line and Angles - Question Paper, Math, Class 9, CBSE - Class 1 PDF Download

 Page 1


30 
 
Chapter - 6 
(Lines and Angles) 
Key Concepts 
(1) Point - We often represent a point by a fine dot made with a fine sharpened 
pencil on a piece of paper. 
(2) Line - A line is completely known if we are given any two distinct points. Line AB 
is represented by as   
      
 . A line or a straight line extends indefinitely in both the 
directions. 
    
 (3) Line segment - A part (or portion) of a line with two end points is called a line 
segment. 
    
 (4) Ray - A part of line with one end point is called a ray. 
    
 (5) Collinear points - If three or more points lie on the same line, they are called 
collinear points otherwise they are called non-collinear points. 
 
Types of Angles - 
(1) Acute angle - An acute angle measure between 0
0
 and 90
0
. 
(2)  Right angle - A right angle is exactly equal to 90
0
. 
(3) Obtuse angle - An angle greater than 90
0
 but less than 180
0
. 
(4) Straight angle - A straight angle is equal to 180
0
. 
(5) Reflex angle - An angle which is greater than 180
0
 but less than 360
0
 is called a 
reflex angle. 
(6) Complementary angles - Two angles whose sum is 90
0
 are called 
complementary angles. 
Page 2


30 
 
Chapter - 6 
(Lines and Angles) 
Key Concepts 
(1) Point - We often represent a point by a fine dot made with a fine sharpened 
pencil on a piece of paper. 
(2) Line - A line is completely known if we are given any two distinct points. Line AB 
is represented by as   
      
 . A line or a straight line extends indefinitely in both the 
directions. 
    
 (3) Line segment - A part (or portion) of a line with two end points is called a line 
segment. 
    
 (4) Ray - A part of line with one end point is called a ray. 
    
 (5) Collinear points - If three or more points lie on the same line, they are called 
collinear points otherwise they are called non-collinear points. 
 
Types of Angles - 
(1) Acute angle - An acute angle measure between 0
0
 and 90
0
. 
(2)  Right angle - A right angle is exactly equal to 90
0
. 
(3) Obtuse angle - An angle greater than 90
0
 but less than 180
0
. 
(4) Straight angle - A straight angle is equal to 180
0
. 
(5) Reflex angle - An angle which is greater than 180
0
 but less than 360
0
 is called a 
reflex angle. 
(6) Complementary angles - Two angles whose sum is 90
0
 are called 
complementary angles. 
31 
 
(7) Supplementary angle - Two angles whose sum is 180
0
 are called 
supplementary angles. 
(8) Adjacent angles - Two angles are adjacent, if they have a common vertex, a 
common arm and their non common arms are on different sides of common arm. 
(9) Linear pair - Two angles form a linear pair, if their non-common arms form  
a line. 
(10) Vertically opposite angles - Vertically opposite angles are formed when two lines 
intersect each other at a point. 
TRANSVERSAL  
(a) Corresponding angles 
(b) Alternate interior angles 
(c) Alternate exterior angles 
(d) Interior angles on the same side of the transversal. 
* If a  transversal intersects two parallel lines, then 
 (i) each pair of corresponding angles is equal. 
 (ii) each pair of alternate interior angles is equal. 
 (iii) each pair of interior angle on the same side of the transversal is 
supplementary. 
* If a transversal interacts two lines such that, either 
 (i) any one pair of corresponding angles is equal, or 
 (ii) any one pair of alternate interior angles is equal or 
 (iii) any one pair of interior angles on the same side of the transversal is 
supplementary then the lines are parallel. 
* Lines which are parallel to a given line are parallel to each other. 
* The sum of the three angles of a triangle is 180
0
. 
* If a side of a triangle is produced, the exterior angle so formed is equal to the 
sum of the two interior opposite angles. 
 
Page 3


30 
 
Chapter - 6 
(Lines and Angles) 
Key Concepts 
(1) Point - We often represent a point by a fine dot made with a fine sharpened 
pencil on a piece of paper. 
(2) Line - A line is completely known if we are given any two distinct points. Line AB 
is represented by as   
      
 . A line or a straight line extends indefinitely in both the 
directions. 
    
 (3) Line segment - A part (or portion) of a line with two end points is called a line 
segment. 
    
 (4) Ray - A part of line with one end point is called a ray. 
    
 (5) Collinear points - If three or more points lie on the same line, they are called 
collinear points otherwise they are called non-collinear points. 
 
Types of Angles - 
(1) Acute angle - An acute angle measure between 0
0
 and 90
0
. 
(2)  Right angle - A right angle is exactly equal to 90
0
. 
(3) Obtuse angle - An angle greater than 90
0
 but less than 180
0
. 
(4) Straight angle - A straight angle is equal to 180
0
. 
(5) Reflex angle - An angle which is greater than 180
0
 but less than 360
0
 is called a 
reflex angle. 
(6) Complementary angles - Two angles whose sum is 90
0
 are called 
complementary angles. 
31 
 
(7) Supplementary angle - Two angles whose sum is 180
0
 are called 
supplementary angles. 
(8) Adjacent angles - Two angles are adjacent, if they have a common vertex, a 
common arm and their non common arms are on different sides of common arm. 
(9) Linear pair - Two angles form a linear pair, if their non-common arms form  
a line. 
(10) Vertically opposite angles - Vertically opposite angles are formed when two lines 
intersect each other at a point. 
TRANSVERSAL  
(a) Corresponding angles 
(b) Alternate interior angles 
(c) Alternate exterior angles 
(d) Interior angles on the same side of the transversal. 
* If a  transversal intersects two parallel lines, then 
 (i) each pair of corresponding angles is equal. 
 (ii) each pair of alternate interior angles is equal. 
 (iii) each pair of interior angle on the same side of the transversal is 
supplementary. 
* If a transversal interacts two lines such that, either 
 (i) any one pair of corresponding angles is equal, or 
 (ii) any one pair of alternate interior angles is equal or 
 (iii) any one pair of interior angles on the same side of the transversal is 
supplementary then the lines are parallel. 
* Lines which are parallel to a given line are parallel to each other. 
* The sum of the three angles of a triangle is 180
0
. 
* If a side of a triangle is produced, the exterior angle so formed is equal to the 
sum of the two interior opposite angles. 
 
32 
 
Section - A  
Q.1 In the given figure,     
 
 
 The value of y is 
 (a) 10
0
   (b) 40
0
   (c) 36
0
   (d) 45
0
 
    
Q.2 An exterior angle of a triangle is 75
0
 and its two interior opposite angles are 
equal. Each of these equal angles is 
 (a) 105
0
  (b) 50.5
0
  (c) 52
0
   (d) 37.5
0
 
Q.3 The compliment of an angle 'm' is: 
 (a) m   (b) 90
0
+m  (c) 90
0
-m  (d) m X 90
0
 
Q.4 If one angle of a triangle is equal to the sum of the other two equal angles, then 
the triangle is  
 (a) an isosceles triangle  (b) an obtuse triangle 
 (c) an equilateral triangle  (d) a right triangle 
Q.5 In the given figure            
 form a linear pair if a-b = 100
0
 
 then a and b are 
 (a) 120
0
, 20
0
   (b) 40
0
, 140
0
 
 (c) 50
0
, 150
0
   (d) 140
0
, 40
0
 
    
Q.6 Angle of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is 
 (a) 60
0
   (b) 40
0
   (c) 80
0
   (d) 20
0
 
Page 4


30 
 
Chapter - 6 
(Lines and Angles) 
Key Concepts 
(1) Point - We often represent a point by a fine dot made with a fine sharpened 
pencil on a piece of paper. 
(2) Line - A line is completely known if we are given any two distinct points. Line AB 
is represented by as   
      
 . A line or a straight line extends indefinitely in both the 
directions. 
    
 (3) Line segment - A part (or portion) of a line with two end points is called a line 
segment. 
    
 (4) Ray - A part of line with one end point is called a ray. 
    
 (5) Collinear points - If three or more points lie on the same line, they are called 
collinear points otherwise they are called non-collinear points. 
 
Types of Angles - 
(1) Acute angle - An acute angle measure between 0
0
 and 90
0
. 
(2)  Right angle - A right angle is exactly equal to 90
0
. 
(3) Obtuse angle - An angle greater than 90
0
 but less than 180
0
. 
(4) Straight angle - A straight angle is equal to 180
0
. 
(5) Reflex angle - An angle which is greater than 180
0
 but less than 360
0
 is called a 
reflex angle. 
(6) Complementary angles - Two angles whose sum is 90
0
 are called 
complementary angles. 
31 
 
(7) Supplementary angle - Two angles whose sum is 180
0
 are called 
supplementary angles. 
(8) Adjacent angles - Two angles are adjacent, if they have a common vertex, a 
common arm and their non common arms are on different sides of common arm. 
(9) Linear pair - Two angles form a linear pair, if their non-common arms form  
a line. 
(10) Vertically opposite angles - Vertically opposite angles are formed when two lines 
intersect each other at a point. 
TRANSVERSAL  
(a) Corresponding angles 
(b) Alternate interior angles 
(c) Alternate exterior angles 
(d) Interior angles on the same side of the transversal. 
* If a  transversal intersects two parallel lines, then 
 (i) each pair of corresponding angles is equal. 
 (ii) each pair of alternate interior angles is equal. 
 (iii) each pair of interior angle on the same side of the transversal is 
supplementary. 
* If a transversal interacts two lines such that, either 
 (i) any one pair of corresponding angles is equal, or 
 (ii) any one pair of alternate interior angles is equal or 
 (iii) any one pair of interior angles on the same side of the transversal is 
supplementary then the lines are parallel. 
* Lines which are parallel to a given line are parallel to each other. 
* The sum of the three angles of a triangle is 180
0
. 
* If a side of a triangle is produced, the exterior angle so formed is equal to the 
sum of the two interior opposite angles. 
 
32 
 
Section - A  
Q.1 In the given figure,     
 
 
 The value of y is 
 (a) 10
0
   (b) 40
0
   (c) 36
0
   (d) 45
0
 
    
Q.2 An exterior angle of a triangle is 75
0
 and its two interior opposite angles are 
equal. Each of these equal angles is 
 (a) 105
0
  (b) 50.5
0
  (c) 52
0
   (d) 37.5
0
 
Q.3 The compliment of an angle 'm' is: 
 (a) m   (b) 90
0
+m  (c) 90
0
-m  (d) m X 90
0
 
Q.4 If one angle of a triangle is equal to the sum of the other two equal angles, then 
the triangle is  
 (a) an isosceles triangle  (b) an obtuse triangle 
 (c) an equilateral triangle  (d) a right triangle 
Q.5 In the given figure            
 form a linear pair if a-b = 100
0
 
 then a and b are 
 (a) 120
0
, 20
0
   (b) 40
0
, 140
0
 
 (c) 50
0
, 150
0
   (d) 140
0
, 40
0
 
    
Q.6 Angle of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is 
 (a) 60
0
   (b) 40
0
   (c) 80
0
   (d) 20
0
 
33 
 
Section - B 
Q.7 Two adjacent angles are equal. Is it necessary that each of these angles will be a 
right angle? Justify your answer. 
Q.8 In the following figures which of the two lines are parallel and why? 
 (i)     (ii)  
   
Q.9 In the given fig. sides QP and RQ of      are produced to point S and T 
respectively. If         
 
 and         
 
 find      
   
Q.10 In the fig.  
 
   
 
        
 
  
 
           
 
          
   
Page 5


30 
 
Chapter - 6 
(Lines and Angles) 
Key Concepts 
(1) Point - We often represent a point by a fine dot made with a fine sharpened 
pencil on a piece of paper. 
(2) Line - A line is completely known if we are given any two distinct points. Line AB 
is represented by as   
      
 . A line or a straight line extends indefinitely in both the 
directions. 
    
 (3) Line segment - A part (or portion) of a line with two end points is called a line 
segment. 
    
 (4) Ray - A part of line with one end point is called a ray. 
    
 (5) Collinear points - If three or more points lie on the same line, they are called 
collinear points otherwise they are called non-collinear points. 
 
Types of Angles - 
(1) Acute angle - An acute angle measure between 0
0
 and 90
0
. 
(2)  Right angle - A right angle is exactly equal to 90
0
. 
(3) Obtuse angle - An angle greater than 90
0
 but less than 180
0
. 
(4) Straight angle - A straight angle is equal to 180
0
. 
(5) Reflex angle - An angle which is greater than 180
0
 but less than 360
0
 is called a 
reflex angle. 
(6) Complementary angles - Two angles whose sum is 90
0
 are called 
complementary angles. 
31 
 
(7) Supplementary angle - Two angles whose sum is 180
0
 are called 
supplementary angles. 
(8) Adjacent angles - Two angles are adjacent, if they have a common vertex, a 
common arm and their non common arms are on different sides of common arm. 
(9) Linear pair - Two angles form a linear pair, if their non-common arms form  
a line. 
(10) Vertically opposite angles - Vertically opposite angles are formed when two lines 
intersect each other at a point. 
TRANSVERSAL  
(a) Corresponding angles 
(b) Alternate interior angles 
(c) Alternate exterior angles 
(d) Interior angles on the same side of the transversal. 
* If a  transversal intersects two parallel lines, then 
 (i) each pair of corresponding angles is equal. 
 (ii) each pair of alternate interior angles is equal. 
 (iii) each pair of interior angle on the same side of the transversal is 
supplementary. 
* If a transversal interacts two lines such that, either 
 (i) any one pair of corresponding angles is equal, or 
 (ii) any one pair of alternate interior angles is equal or 
 (iii) any one pair of interior angles on the same side of the transversal is 
supplementary then the lines are parallel. 
* Lines which are parallel to a given line are parallel to each other. 
* The sum of the three angles of a triangle is 180
0
. 
* If a side of a triangle is produced, the exterior angle so formed is equal to the 
sum of the two interior opposite angles. 
 
32 
 
Section - A  
Q.1 In the given figure,     
 
 
 The value of y is 
 (a) 10
0
   (b) 40
0
   (c) 36
0
   (d) 45
0
 
    
Q.2 An exterior angle of a triangle is 75
0
 and its two interior opposite angles are 
equal. Each of these equal angles is 
 (a) 105
0
  (b) 50.5
0
  (c) 52
0
   (d) 37.5
0
 
Q.3 The compliment of an angle 'm' is: 
 (a) m   (b) 90
0
+m  (c) 90
0
-m  (d) m X 90
0
 
Q.4 If one angle of a triangle is equal to the sum of the other two equal angles, then 
the triangle is  
 (a) an isosceles triangle  (b) an obtuse triangle 
 (c) an equilateral triangle  (d) a right triangle 
Q.5 In the given figure            
 form a linear pair if a-b = 100
0
 
 then a and b are 
 (a) 120
0
, 20
0
   (b) 40
0
, 140
0
 
 (c) 50
0
, 150
0
   (d) 140
0
, 40
0
 
    
Q.6 Angle of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is 
 (a) 60
0
   (b) 40
0
   (c) 80
0
   (d) 20
0
 
33 
 
Section - B 
Q.7 Two adjacent angles are equal. Is it necessary that each of these angles will be a 
right angle? Justify your answer. 
Q.8 In the following figures which of the two lines are parallel and why? 
 (i)     (ii)  
   
Q.9 In the given fig. sides QP and RQ of      are produced to point S and T 
respectively. If         
 
 and         
 
 find      
   
Q.10 In the fig.  
 
   
 
        
 
  
 
           
 
          
   
34 
 
Q.11 Sum of two angles of a triangle is 90
0
 and their difference is 50
0
. Find all the 
angles of the triangle. 
Q.12 In the adjoining figure,         find the value of      . 
  
 
Section - C 
Q.13 In the given figure AB and CD intersect each other at O. If        
 
 find the 
value of            
  
Q.14 Prove that vertically opposite angle are equal. 
Q.15 In the given figure             prove that