Class 7 Maths Chapter 6 HOTS Questions - Lines and Angles

Q1: The angles x – 10 degree and 190 – x are
(i) interior angles present on the same side of the transversal
(ii) making a linear pair
(iii) complementary
(iv) supplementary
Ans:-(iv) supplementary

When the sum of the measures of these two angles is 180 degree, then the angles are called as supplementary angles.
x – 10 + 190 – x = 180
190 – 10 = 180
180 = 180
LHS = RHS

Q2: The measure of the angle which is four times of its own supplement angle is
(a) 36
(b) 144
(c) 16
(d) 64
Ans:- (b) 144

We know that the final sum of measures of the two angles is 180 degrees, then the angles are called supplementary angles.
Let us assume that the angle is x.
Then, its supplement angle is = (180 – x)
As per the condition given in the above question, x = 4 (180 – x)
x = 720 – 4x
x + 4x = 720
5x = 720
x = 720/5
x =144

Q3: If the two supplementary angles are in the ratio of 1: 2, then the bigger angle is of
(a) 120
(b) 125
(c) 110
(d) 90
Ans:-(a) 120

We know that the sum of the measures of the two angles is 180 degrees, then the angles are called the supplementary angles.
Let us assume that the two angles be 1x and 2x.
1x + 2x = 180
3x = 180
x = 180/3
x = 60
Then the bigger angle is 2x = 2 × 60 = 120

Q4: In a pair of adjacent angles, the,  
(i) vertex is always common,
(ii) one arm is always common, and
(iii) uncommon arms are always opposite rays
So,
(a) All the statements (i), (ii) and (iii) are true
(b) The statement (iii) is false
(c) The statement (i) is false, but the statements (ii) and (iii) are true
(d)The statement (ii) is false
Ans:- (b)The statement (iii) is false

Two angles are called adjacent angles only if they contain a common vertex and arm but no other common interior points.

Q5: In the below questions, fill in the blanks to make the below statements true.
(i) If the sum of the measures of the two angles present is 90 degrees, then the angles are _________.
Ans:- If the sum of measures of the two angles is 90 degrees, then these angles are complementary angles.

(ii) If the sum of measures of the two angles is degrees 180 , then they are _________.
Ans:- If the sum of measures of the two angles is 180 degrees, then they are supplementary angles.

(iii) A transversal that intersects two or more than the two lines at _________ points.
Ans:- A transversal always intersects two or more two lines at distinct points.

Q6: If the angle P and angle Q are supplementary angles and the measure of angle P is 60 degrees, then the measure of the angle Q is
(a) 120 
(b) 60 
(c) 30 
(d) 20
Ans:- (a) 120 

When the sum of the measures of these two angles is 180 degree, then the angles are called the supplementary angles.
P + Q = 180
60 + Q = 180
Q = 180 – 60
Q = 120

Q7: The difference found between the two complementary angles is 30 degrees. Then, the angles present are
(a) 60, 30
(b) 70, 40
(c) 20, 50
(d) 105, 75
Ans:-(a) 60, 30

When the sum of the measures of the two angles is 90 degrees, then the angles are called the complementary angles.
So, 60 + 30 = 90
As per the condition in the question, 60 – 30 = 30

Q8: Statements a and b are given below:
Statement a: If the two lines intersect at each other, then the vertically opposite angles present are equal in nature.
Statement b: If a transversal line intersects the two other lines, then the sum of the two interior angles present on the same side of the transversal is 180 degrees.
Then
(a) Both statements a and b are true
(b) Statement a is true while the statement b is false
(c) The statement a is false, and b is true
(d) Both statements a and b are false
Ans:- (a) Both statements a and b are true.

Statement a: This is true. When two lines intersect, the angles that are vertically opposite each other are always equal. This is a fundamental property of intersecting lines.

Statement b: This is also true. When a transversal intersects two lines, the interior angles on the same side of the transversal (called consecutive or co-interior angles) add up to 180 degrees if the two lines are parallel. This is a property of parallel lines and transversals.

Q9: If an angle is 60 degrees less than the two times of its supplement, then the greater angle is of
(a) 100
(b) 80
(c) 60
(d) 120
Ans:- (a)100

Let us assume the angle is P.
Then, its supplement is 180 – P
As per the condition in the question,
P = 2(180 – P) – 60
P = 360 – 2P – 60
P + 2P = 300
3P = 300
P = 300/3
P = 100
So, its supplement is 180 – P = 180 – 100 = 80
Therefore, the greater angle is 100.

Q10: If a transversal intersects the two parallel lines, then [from (a) to (d) ].
(i) The sum of the interior angles present on the similar side of a transversal is __________.
Ans:- The Sum of interior angles on the similar side of a transversal is 180.

(ii) Alternate interior angles have one common__________.
Ans:- Alternate interior angles have one common arm.

(iii) Corresponding angles are on the__________ side of the transversal.
Ans:- Corresponding angles are on the similar side of the transversal.

(iv) Alternate interior angles are on the __________side of the transversal.
Ans:- Alternate interior angles are present on the opposite side of the transversal.

(v) Two lines that are present in a plane which does not meet at a given point anywhere are called __________lines.
Ans:- Two lines present in a plane which do not meet together at a given point anywhere are called parallel lines.

(vi) Two angles forming a __________ pair are supplementary.
Ans:- Two angles forming a linear pair are supplementary

(vii)  The supplement of an acute is always __________ angle.
Ans:- The supplement angle of an acute angle is always called an obtuse angle.

(viii) The supplement of a right angle is always _________ angle.
Ans:- The supplement angle of the right angle is always the right angle.

(ix) The supplement of an obtuse angle is always _________ angle.
Ans:- The supplement angle of an obtuse angle is always called an acute angle.

(x) In a pair of complementary angles, each of these angles cannot be more than _________.
Ans:- In the pair of complementary angles, each angle present cannot be more than 90.

(xi) An angle is 45^o. Its complementary angle will be __________.
Ans:- An angle is 45^o. Its complementary angle will be 45.

(xii) An angle which is half of its supplement is of __________.
Ans:- An angle which is half of its supplement angle is the angle of 60.
Let us assume that the angle is p, and the supplement is 2p
Hence, p + 2p = 180
3p = 180
p = 60