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

### Question 1

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∘

So, adding these

∠A+∠B+∠C+∠D+∠E+∠F=180∘+180∘=360∘

### Question 2

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

180∘

270∘

360∘

540∘

#### SOLUTION

Solution :C

By angle sum property,

x+y+z=180∘

∠BAF+∠ACD+∠CBE

=(180∘−x)+(180∘−y)+(180∘−z)

=540∘−(x+y+z)=540∘−180∘=360∘

### Question 3

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

45∘

55∘

60∘

70∘

#### SOLUTION

Solution :B

From the given figure,

∠ECD=180∘−150∘=30∘ (sum of interior angles on the same side of the transversal is 180°)

x=∠BCD=25∘+∠ECD (alternate interior angles)

=25∘+30∘=55∘

### Question 4

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

True

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∘

### Question 5

Which one of the following statements are true?

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

Angles forming a linear pair can both be acute angles.

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

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∘ .

### Question 6

In the figure below, the value of x∘ is:

15o

60o

30o

20o

#### SOLUTION

Solution :C

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

6x = 180∘

x = 30∘

### Question 7

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

60∘

65∘

40∘

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∘

### Question 8

Two parallel lines have:

#### SOLUTION

Solution :C

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

### Question 9

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∘.

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

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

Statement 1 is true and statement 2 is false.

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.

### Question 10

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

45∘

25∘

5∘

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∘