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 = 110o and ∠QRS = 130o, 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∘