# Free Lines and Angles 02 Practice Test - 9th Grade

In the adjoining figure, the value of A+B+C+D+E+F in degrees is

___ #### SOLUTION

Solution :

From ABC;

A+B+C=180

From DEF;

D+E+F=180

A+B+C+D+E+F=180+180=360

The sides BC, CA and AB of ΔABC are produced in order to form exterior angles ACDBAF and  CBE respectively, then BAF+ACD+CBE  is

A.

180

B.

270

C.

360

D.

540

#### SOLUTION

Solution : C By angle sum property,
x+y+z=180
BAF+ACD+CBE
=(180x)+(180y)+(180z)
=540(x+y+z)=540180=360

In the figure given below, find x if AB || CD. A.

45

B.

55

C.

60

D.

70

#### SOLUTION

Solution : B

From the given figure,

ECD=180150=30 (sum of interior angles on the same side of the transversal is 180°)

x=BCD=25+ECD (alternate interior angles)
=25+30=55

In the given figure,if yx=5 and zx=4 , then the value of x is 12. A.

True

B.

False

#### SOLUTION

Solution : B

yx=5
y=5x and
zx=4
z=4x
x+y+z=180
x+5x+4x=180
10x=180
x=18

Which one of the following statements are true?

A.

If two angles form a linear pair, then each of these angles is of measure 180.

B.

Angles forming a linear pair can both be acute angles.

C.

One of the angles forming a linear pair can be obtuse angle.

D.

The sum of the angles of a linear pair is 180.

#### SOLUTION

Solution : C and D

If two angles form a linear pair, either both of them are 90 or one angle is acute and the other is obtuse. They cannot both be acute angles because in that case the sum would not be 180 .

In the figure below, the value of x is: A.

15o

B.

60o

C.

30o

D.

20o

#### SOLUTION

Solution : C

x + 2x + 3x = 180 [Angles on a straight line]

6x = 180

x = 30

In the figure given below, if OP || RS, ∠OPQ = 110o and ∠QRS = 130o, then ∠PQR is equal to A.

60

B.

65

C.

40

D.

45

#### SOLUTION

Solution : A

Extend OP. Then, a triangle PQT will be formed; where T is the point at which OP cuts QR. Now,

OPQ + QPT = 180

QPT = 180 - 110 = 70

Now, since if OP || RS,  SRQ and UTQ are corresponding angles hence, UTQ = SRQ = 130

Therefore we have,

UTQ + PTQ = 180

PTQ = 180 - 130 = 50

In triangle PTQ,

PTQ + TQP + QPT = 180

50 TQP + 70 = 180

TQP = 180 - 120 = 60

TQP = PQR = 60

Two parallel lines have:

A. A common point
B. Two common points
C. No common point
D. Infinite common points

#### SOLUTION

Solution : C Parallel lines never intersect. Hence, they have no common point.

With reference to the figure below, consider the two statements:

Statement 1: The points A, B, and C will lie on a straight line if x + y = 180.

Statement 2: The angle on a straight line is 180. A.

Both the statements are true and statement 2 is the correct explanation of statement 1.

B.

Both the statements are true and statement 2 is not the correct explanation of statement 1.

C.

Statement 1 is true and statement 2 is false.

D.

Statement 1 is false and statement 2 is true.

#### SOLUTION

Solution : A

The angle on a straight line is 180. Adjacent angles on a straight line add up to 180.

Conversely, if adjacent angles add up to 180 then the angles are on a straight line.

Hence, if x + y = 180 , then A, B and C lie on a straight line.

Therefore, both the statements are true and statement 2 is the correct explanation of statement 1.

Assume line m and line n are parallel lines cut by the transversal line l.  Find the value of x. A.

45

B.

25

C.

5

D.

60

#### SOLUTION

Solution : B

Since, the sum of co-interior angles (interior angles on the same side) = 180

x + 15 + 6x - 10 = 180

7x + 5 = 180

7x = 175

x = 25