Class 9 Maths Chapter 6 Question Answers - Lines and Angles

Q1: Find the angles which are equal to the complement angle.
Ans: Let the measure of a required angle be x degrees.
So, we know that the sum of measures of the complementary angle pair is 90.
Then,
= x + x = 90
= 2x = 90
= x = 90/2
= x = 45
Hence, the required angle measure is 45.

Q2: Can two angles be supplementary angles if both of them are:
(i). Acute?
Ans: No. If two angles are acute angles, it means it is less than 90, which means that the two angles cannot be the supplementary angle because their sum will always be less than 90.
(ii). Obtuse?
Ans: No. If the two angles are obtuse, then it means more than 90, so the two angles cannot be the supplementary angle. Because their sum will always be more than 180.
(iii). Right?
Ans: Yes. If the two angles are right, which means both measure 90, then two angles can form a supplementary pair.
∴ 90  +  90 = 180

Q3: Fill in the following blanks:
(i) If the two angles are known as complementary angles, the sum of their measures is _______.
Ans: If the two angles are known as complementary angles, the sum of their measures is 90 degrees.
(ii) If the two angles are known as supplementary, so the sum of their measures is ______.
Ans: If two of these angles are supplementary angles, then the sum of the measures is 180 degrees.
(iii) Two angles that form a linear pair are known as _________.
Ans: Two angles forming a linear pair are called the Supplementary angle.
(iv) If the two adjacent angles are supplementary, they form a ___________.
Ans: If the two adjacent angles are supplementary angles, then they form a linear pair.
(v) If the two lines intersect at a given point, then the vertically opposite angles are always______
Ans: If two lines intersect at a given point, then the vertically opposite angles present are always equal.
(vi) If two lines intersect at a given point, and if one pair of the vertically opposite angles are the acute angles, then the other pair of the vertically opposite angles are __________.
Ans: If two lines intersect at a given point, and if one of the pair of the vertically opposite angles are the acute angles, then the other pair of the vertically opposite angles are Obtuse angles.

Q4: Angles which are both supplementary as well as vertically opposite are
(i) 95, 85 
(ii) 90, 90 
(iii) 100, 80 
(iv) 45, 45
Ans: (b) 90, 90
When the sum of the measures of the two angles is 180 degree, then the angles are called as supplementary angles.

Q5: The angles x degree and 90 – x are
(i) supplementary
(ii) complementary
(iii) vertically opposite
(iv), making a linear pair
Ans: (ii) complementary angle
When the sum of the measures of the two angles is 90 degree, then the angles are called complementary angles.
x + 90 – x = 90
90 = 90
LHS = RHS

Q6: Identify which of these following pairs of angles are complementary to each other and which of these angles are supplementary.
(i) 65, 115
Ans: We have to find the sum of all the given angles to identify whether these angles are complementary or supplementary.
Now,
= 65 + 115
= 180
If the sum of the two angle measures is 180, then these two angles are said to be supplementary.
Hence, These angles are termed supplementary angles.
(ii) 63, 27
We have to find the final sum of the given angles to identify whether these angles are complementary or supplementary.
So,
= 63 + 27
= 90
If the total sum of the two angle measures is 90, then these two angles are said to be complementary.
Hence, These angles are complementary angles.
(iii) 112, 68
We have to find the sum of all the given angles to identify whether these angles are complementary or supplementary.
Then,
= 112 + 68
= 180
If the sum of the two angle measures is 180 degrees, then the two angles are said to be a supplementary.
Hence, These angles are supplementary angles.
(iv) 130, 50
We have to find the sum of all the given angles to identify whether these angles are complementary or supplementary.
Then,
= 130 + 50
= 180
If the sum of the two angle measures is 180 degrees, then these two angles are said to be supplementary to each other.
∴ These angles are supplementary angles.
(v) 45, 45
We have to find the sum of the given angles to identify whether these angles are complementary or supplementary.
Then,
= 45 + 45
= 90
If the sum of the two angle measures is 90, then the two angles are said to be complementary.
∴ These angles are complementary angles.
(vi) 80, 10
We have to find the sum of the given angles to identify whether these angles are complementary or supplementary.
Then,
= 80 + 10
= 90
If the sum of the two angle measures is 90 degrees, then the two angles are said to be a complementary angles.
Hence, These angles are complementary angles.

Q7: Determine the angle which is equal to its own supplement angle.
Ans: Let the measure of required angle be x degrees.
We know that the total sum of the measures of the supplementary angle pair is 180.
Then,
= x + x = 180
= 2x = 180
= x = 180/2
= x = 90
Hence, the required angle measure is 90.

Q8: An angle is greater than 45 degrees. Is its complementary angle greater than degree 45 or equal to 45 or less than degree 45?
Ans: Let us assume that the complementary angles are p and q,
We know the sum of the measures of the complementary angle pair is 90.
Then,
= p + q = 90
It is given in the above question that p > 45
Adding q on both sides,
= p + q > 45 + q
= 90 > 45 + q
= 90 – 45 > q
= q < 45
Hence, its complementary angle is less than degree 45.

Q9:  If the complement of an angle is 79 degrees, then the angle will be
(i) 1
(ii) 11
(iii) 79
(iv) 101
Ans: (ii) 11
When the sum of the measures of any two angles is 90 degree, then the angles are called complementary angles. Each of them complements the other.
The given complement of an angle is 79
Let the measure of the angle be in degree x.
Then,
x + 79 = 90
x = 90 – 79
x = 11
Hence, the measure of the angle is 11.

Q10: The angle which makes a linear pair with an angle of 61 degree is of
(i) 29
(ii) 61
(iii) 122
(iv) 119
Ans: (d) 119
A linear pair is a pair of adjacent angles whose non-common sides are the opposite rays.
We know that the measure of the sum of the adjacent angles is always equal to 180.
Let the measure of the other angle be x.
Then,
x + 61 = 180
x = 180 – 61
x = 119