Free Lines and Angles Subjective Test 02 Practice Test - 7th grade 

Question 1

What do we mean by supplementary angles?  [1 MARK]


Solution :

Two angles are supplementary if their sum is equal to 180.

Question 2

Find the complement of the following angles. [2 MARKS]
(b) 32


Solution :

Each Part: 1 Mark

Sum of complementary angle is equal to 

Therefore, the complement of:

(a)  65

(b) 32

Question 3

(a) Find the angle which is supplementary to itself. 
(b) Find the angle which is double its supplement.


Solution :

Solution: 1 Mark each

(a) Let the angle be x.

therefore its supplement  =  x  (as the supplementary angles are equal)

Sum of supplementary angles is  180



(b) Let the angle be x.
Its supplement = 2x.

Sum of supplementary angles is  180

The angle which is double its supplement = 2x = 120

Question 4

(a) What kind of numbers do you get if you add consecutive triangular numbers? Give examples. 
(b) Complement of E is F, if E= 28, find F.


Solution :

Each part: 1 Mark

(a) By adding consecutive triangular numbers, we get square numbers.
e.g. 1 + 3 = 4, 6 + 10 = 16, etc.

(b)  F=9028  (Sum of complementary angles is 90)

Question 5

In the given figure, show that 1+3+8+6=3600. [2 MARKS]


Solution :

Proof: 2 Marks

1+2+3+4=3600  [Angles about a point]

4=8    [Pair of corresponding angles]
and 2=6   [Pair of corresponding angles]


Question 6

How are angles classified based on their measure? [3 MARKS]


Solution :

Acute Angle: 1 Mark
Right Angle: 1 Mark
Obtuse Angle: 1 Mark

Angles are classified based on their measure as:

(i) Acute Angle: An angle that is > 0 and < 90 is called an acute angle.

(ii) Right Angle: An angle that is exactly equal to 90, is called a right angle.

(iii) Obtuse Angle: An angle that is > 90 and < 180, is called an obtuse angle.

Question 7

(a) What are the three conditions that must be satisfied for two angles to be adjacent? [3 MARKS]

In the given figure, 1 and 2 are supplementary angles. If 1 decreases, then 2  will _______  so that both the angles are still supplementary.


Solution :

(a) Conditions: 2 Marks
(b) Explanation: 1 Mark

(a) Two angles are said to be adjacent if they have:   

      i) Common vertex

     ii) Common arm

    iii) Non-common arms are on either side of the common arm

If  1 decreases then, 2 will increase by the same measure, so that both the angles are still supplementary.

Question 8

(a) Can a triangle have two obtuse angles? Justify your answer.
(b) In a ABC the side BC is extended to D. Given that ABC=30 and ACD=160. Find BAC. [3 MARKS]


Solution :

(a) Answer: 1 Mark
     Reason: 1 Mark
(b) Solution: 1 Mark

(a) A triangle can have only one obtuse angle.

If we have more than one obtuse angle in a triangle, then the sum of two (obtuse) angles will exceed 180

Since the sum of all angles of a triangle is 180

A triangle cannot have more than one obtuse angle.


BCD=180 (Straight angle)

Question 9

(a) There are two sets of parallel lines passing through a plane. A transversal cuts the two sets of lines. Find the number of distinct points of intersection.

(b)  The following diagram shows parallel lines cut by a transversal. Find x. [3 MARKS]


Solution :

(a) Solution: 1 Mark
(b) Application of concept: 1 Mark
     Correct Answer: 1 Mark

(a) There are 4 points of intersection between the parallel lines & transversal.

 In the above figure since the two lines are parallel and cut by a transversal, using the property of corresponding angles:

=> 2x - 60 = x

=> x - 60 = 0

=> x = 60

Question 10

 (a) Find the value of x, if l is parallel to m and a is parallel to b.

(b)Find the value of x.



Solution :

Each part: 2 Marks

(a) Given, ab and lm

Mark an angle 1 in the figure.

1=80   [Corresponding angles]

1 + x= 180 [Since lm,1 and x are cointerior angles]



(b) 5=5x+35          (Alternate angles)
 45+5=180     (Linear pair)


Question 11

(a) Find the number of line segments in the following figure.  

 Find the values of angles x, y and z in each of the following:




Solution :

(a) Correct answer: 1 Mark 
(b) Each angle: 1 Mark


The total number of line segments is 8. The line segments are AF, AB, BF, FD, FC, CD, AC and BD.

 (i) x and 55 are vertically opposite,

x = 55

x + z = 180

55 + y = 180

y = 180  –  55  =  125

y = z  (Vertically Opposite angles)

z = 125

(ii) z = 40 (Vertically opposite angles)

y + z = 180

y = 18040140

40 + x + 25 = 180

65 + x  =  180

x = 18065  =  115

Question 12

From the given figure, find ADG and IEJ. ABCD is a rectangle. [4 MARKS]


Solution :

Steps: 2 Marks
Each angle: 1 Mark

Since ABCD is a rectangle, ABCD

EDC=EIJ=50 (Corresponding Angles).

Since ABCD is rectangle, ADC=90



EJI=180105=75 (Linear pair);

IEJ=180(75+50) (Angle sum property)


Question 13

In the given figure, ΔAEC and ΔDBF are equilateral. Prove that all the other triangles are also equilateral. (Given that bases of the triangles are parallel).  [4 MARKS]


Solution :

Steps: 3 Marks
Proof: 1 Mark

 ΔAEC and ΔDBF are equilateral, therefore angle made at each vertex is =60

Consider ΔAMN,


AEC=AMN=60  (Corresponding Angles as FBEC)

Similarly ACE=ANM=60   (Corresponding Angles).

Hence all angles of ΔAMN are equal to 60 and is an equilateral triangle.

Consider ΔBNO, FBD=60 

BNO=ANM=60  (vertically Opposite Angles)

BON=60  (Angle sum property of triangle).

Hence ΔBNO is also equilateral.
Similarly, we can prove it for the remaining triangles

Question 14

(a) In the given figure, the base of the triangle is parallel to line l and 1=2. Prove that line BC & m are parallel to each other.

Consider the following figure. Find the angle y.



Solution :

(a) Steps: 1 Mark
     Proof: 1 Mark
(b) Steps: 1 Mark
     Correct Answer: 1 Mark

 1=2   (given)  
They are also corresponding angles. 

lm...(i)  (If corresponding angles are equal, then the lines are parallel)

Also, lBC....(ii)  

From (i) and (ii):



 In ΔBDA, x + x + y = 180 (by angle sum property)
similarly, in ΔBDC, x + x + BDC = 180
Comparing the two equations, we have BDC = y.
Also, BDC + BDA = 180 (linear pair)
or, y + y = 180
or, y = 90

Question 15

In the adjoining figure, pq. Find the unknown angles. [4 MARKS]



Solution :

Application of theorems: 1 Mark
Steps: 1 Mark
Correct answers: 2 Marks

Given p  q 

125+e=180     [Linear pair]

e=180125=55   (i)

e=f=55    [Vertically opposite angles]

a=f=55     [Alternate interior angles] 

a+b=180     [Linear pair]

55+b=180  [From eq. (i)]


a=c=55 , b=d=125  [Vertically opposite angles]

a=55, b=125

c=55, d=125, e=55, f=55.