# Free Lines and Angles Subjective Test 01 Practice Test - 7th grade

Find the angle which is complementary to itself. [1 MARK]

#### SOLUTION

Solution :

Given - the complementary angles are equal.

Let the angle be x. So its complement  = x.

x+x=90

2x=90

x=45

The angle which is complementary to itself is x=45.

State at least two differences between a line and a line segment. [2 MARKS]

#### SOLUTION

Solution :

Each difference: 1 Mark

1. A line is a set of points that can be extended in either direction whereas a line segment is a part of a line, which is bounded between two given points.
2. Length of a line segment can be measured, whereas a line can extend up to infinity and cannot be measured.

If the number of endpoints in a line, ray and a line segment are represented by X, Y, and Z, then find the value of X + Y + Z [2 MARKS]

#### SOLUTION

Solution :

Steps: 1 Mark
Result: 1 Mark

The number of endpoints in a line is zero.

X=0

The number of endpoints in a Ray is 1

Y=1

The number of endpoints in a line segment is 2.

Z=2

X+Y+Z=3

Find the supplementary angles corresponding to all the angles of a right angle isosceles triangle [2 MARKS]

#### SOLUTION

Solution :

Steps: 1 Mark

The angles of a right-angled isosceles triangle are:

90, 45  and  45.

Hence the supplementary angles are:

18090=90

18045=135

18045=135

(a) In the given figure, the value of x is: [2 MARKS] (b) An angle is greater than 45
. Its complement  is ____  (>,<, = ) 45.

#### SOLUTION

Solution :

Solution: 1 Mark each

(a) Sum of the angles should be equal to
360

110+60+40+x=360

210+x=360

x=360210=150

(b) Let A and B be two complementary angles and let A >  45.

A + B =  90

B = 90 − A

Therefore, B will be less than 45.

(a) Prove that when two lines intersect, the vertically opposite angles are equal.
(b)
Find the value of x from the given figure: [3 MARKS] #### SOLUTION

Solution :

(a) Proof: 2 Marks
(b) Solution: 1 Mark

(a) We have to prove 1=3 & 2=4

1+2=180              [Linear pair]

1=1802

Again, 3+2=180       [Linear pair]

3=1802

Hence, 1=3

Similarly, we can prove that 2=4.

(b)
AOB = DOE    (vertically opposite angles)
x = 60

In the given figure, CO = OD & OCD=30. Find AOB? [3 MARKS] #### SOLUTION

Solution :

Concept: 1 Mark
Steps: 1 Mark

Sum of the angles of a triangle is 180.

Since OC = OD,  OCD=ODC=30
[Angles opposite to equal sides are equal]

COD=180(30+30)=120

AOB=COD  [Vertically Opposite Angles]

AOB=120

(a) In the given figure, prove that LXMYNZ.  [3 MARKS] (b) If k=50, then find the value of PSY.

#### SOLUTION

Solution :

(a) Steps: 1 Mark
Proof: 1 Mark

(b) Solution: 1 Mark

(a) XPB=MSP=k  (Alternate Angles are equal)

LXMY...(i).

PSM=SRN=k  (Corresponding Angles)

MYNZ....(ii).

From (i) and (ii)

LXMY  and  MYNZ

LXMYNZ.

(b) Given  k=50,

PSY=180k

=18050=130

(a) In the given figure, prove that lines lm & nq are parallel to each other. (b) Find the value of "x” if AB is parallel to CD. [3 MARKS]

#### SOLUTION

Solution :

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

(a) Given, LST=105 and NTS=75

LST+NTS=105+75=180

These are co-interior angles.

Since co-interior angles are supplementary, lines are parallel.

Hence, the lines LM and NQ are parallel.

(b) Since AB is parallel to CD, corresponding angles will be equal.

Therefore, x = 130°

(a) Find out the unknown BOD in the given quadrilateral ABDC in which ABCD. Given that AD & BC are angle bisectors of  BAC & DCA respectively. (b)
What is the value of (x+y) in the figure below? [4 MARKS]

#### SOLUTION

Solution :

(a) Steps: 2 Marks
Result: 1 Mark
(b) Solution: 1 Mark

(a) Since ABCD

BAC+DCA=180

[Sum of Co-interior angles is equal to 180]

BAC2+DCA2=1802

OAC+OCA=90   [AD & BC are angle bisectors]

In ΔAOC,

AOC+OAC+OCA=180

[sum of  all the angles in triangle is 180]

AOC=18090=90

AOC=BOD  [Vertically Opposite Angles]

BOD=90

(b)
The value of an exterior angle of a triangle is equal to the sum of the opposite interior angles.

As the exterior angle value is given to be 120, the sum of the two interior angles is also 120.
Thus, (x+y) = 120

In the given figure, find the value of BAC. ΔDEF is equilateral, CBA=40, FEC=50 and DE is parallel to BC. [4 MARKS] #### SOLUTION

Solution :

Steps: 3 Marks
Result: 1 Mark

Given  DEBC,CBA=40

Since, ΔDEF is equilateral

DEF=60

FEC=50   (Given)
AED=180(50+60)     (Angles on a straight line)
= 70

DAE=180(70+40)=70.

BAC=DAE=70. (a) Lines AB & CD are parallel and cut by a transversal tList the alternate, corresponding, co-interior and vertically opposite angles. (b) (i) l and m are parallel lines and t is the transversal. Find x

(ii) l and m are parallel lines and t is the transversal. Find x.
[4 MARKS]

#### SOLUTION

Solution :

(a) Solution: 2 Marks
(b) Each part: 1 Mark

(a) Corresponding Angles

1=5,3=7,2=6,4=8;

Vertically Opposite Angles:

1=4,2=3,5=8,6=7;

Alternate Interior Angles:

3=6,4=5;

Alternate Exterior Angles:

1=8,2=7;

Co-interior Angles:

4,6,3,5.

(b) (i) x=60 (Alternate Angles)

(ii) x=120 (Corresponding Angles)

(a) From the given figure find the value of 'x'.  [4 MARKS] (b) In the figure below, x = 30. The value of (6y – 3x) is ___. #### SOLUTION

Solution :

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

(a) 40+4x+3x=180  [since POQ is a straight line]

7x=18040

x=1407=20

Hence, the value of 'x' is

x=20

(b) Given, x = 30,

So, 2x=60

Also, 2x+3y=180  (linear pair)

Replacing x in the above equation,
60+3y=180

3y=120

y=40

The value of 6y3x=150

Classify the following pair of angles as complementary and supplementary. [4 MARKS]

(i) 120,50

(ii) 60,120

(iii) 39,61

(iv) 65,25

#### SOLUTION

Solution :

Each part: 1 Mark

Two angles are complementary when they add up to 90

Two angles are supplementary when they add up to 180

(i) 120+50=170

Angles are neither complementary nor supplementary.

(ii) 60+120=180

Angles are supplementary.

(iii) 39+61=100

Angles are neither complementary nor supplementary.

(iv) 65+25=90

Angles are complementary.

(a) Find the value of angles 2,3,4 if 1 is 45.  [4 MARKS] (b) The supplement of which angle is the complement of 70?

#### SOLUTION

Solution :

(a) Steps: 1 Mark
Angles: 1 Mark
(b) Steps: 1 Mark
Result: 1 Mark

(a) Given 1=45

3=1=45    [Vertically opposite angle]

2+3=180   [Linear pair]

2+45=180

2=18045

2=135

2=4   [Vertically opposite angle]

4=2=135

(b) Let the angle be x

its supplementary angle = (180x)

Given that (180x) is the complementary angle of 70

(180x)+70=90

x=18020

x=160
The required angle is 160.