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

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

#### SOLUTION

Solution :

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

Find the complement of the following angles. [2 MARKS]
(a)
65
(b) 32

#### SOLUTION

Solution :

Each Part: 1 Mark

Sum of complementary angle is equal to
90.

Therefore, the complement of:

(a)  65
9065=25

(b) 32
9032=58

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

#### SOLUTION

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

x+x=180

x=90

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

Sum of supplementary angles is  180
x+2x=180
3x=180
x=60

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

(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.
[2 MARKS]

#### SOLUTION

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)
=62

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

Solution :

Proof: 2 Marks 4=8    [Pair of corresponding angles]

and 2=6   [Pair of corresponding angles]

1+3+8+6=3600

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

#### SOLUTION

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.

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

(b)
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

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

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

(b) In a ABC the side BC is extended to D. Given that ABC=30 and ACD=160. Find BAC. [3 MARKS]

#### SOLUTION

Solution :

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.

(b) BCD=180 (Straight angle)
ACB=BCDACD=(180160)=20
BAC=180(ABC+ACB)=180(30+20)=18050=130
BAC=130

(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

Solution :

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

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

(a) Find the value of x, if l is parallel to m and a is parallel to b. (b)Find the value of x. [4 MARKS]

#### SOLUTION

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]

x=18080

x=100

(b) 5=5x+35          (Alternate angles)
45+5=180     (Linear pair)
5=18045
=135

5x+35=135
5x=13535=100
x=1005=20

(a) Find the number of line segments in the following figure. (b)
Find the values of angles x, y and z in each of the following: [4 MARKS]

#### SOLUTION

Solution :

(b) Each angle: 1 Mark

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

(b)
(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

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

Solution :

Steps: 2 Marks
Each angle: 1 Mark Since ABCD is a rectangle, ABCD

EDC=EIJ=50 (Corresponding Angles).

EJI=180105=75 (Linear pair);

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

IEJ=55.

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

Solution :

Steps: 3 Marks
Proof: 1 Mark ΔAEC and ΔDBF are equilateral, therefore angle made at each vertex is =60

Consider ΔAMN,

MAN=60

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

(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. (b)
Consider the following figure. Find the angle y. [4 MARKS]

#### SOLUTION

Solution :

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

mlBC.

mBC.

(b)
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

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

Solution :

Application of theorems: 1 Mark
Steps: 1 Mark

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)]

b=18055=125

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

a=55, b=125

c=55, d=125, e=55, f=55.