NCERT Solution For Class Class 7, Maths, Lines And Angles, Exercise 5.1 has total fourteen question to practice. Ex 5.1 class 7 is basically about acute, obtuse and Right angle figure in which students need to find required angles. Class 7 maths chapter 5 exercise 5.1 is given below.
NCERT Solution For Class Class 7, Maths, Lines And Angles, Exercise 5.1
Exercise 5.1, Class 7
Q.1. Find the complement of each of the following angles:
Ans: Two angles are said to be complementary if the sum of their measures is 90o.
∴ Complementary angle = 900 – Given angle
(i) Complement of 630 = 900 – 630 = 270
(ii) Complement of 200 = 900 – 200 = 700
(iii) Complement of 570 = 900 – 570 = 330
Q.2. Find the supplement of each of the following angles:
Ans: Two angles are said to be supplementary if the sum of their measures is 180o.
∴ Supplementary angle = 1800 – Given angle
(i) Supplement of 1050 = 1800 – 1050 = 750
(ii) Supplement of 870 = 1800 – 870 = 930
(iii) Supplement of 1540 = 1800 – 1540 = 260
Q.3. Identify which of the following pairs of angles are complementary and which are supplementary.
(i) 65º, 115º (ii) 63º, 27º (iii) 112º, 68º (iv) 130º, 50º (v) 45º, 45º (vi) 80º, 10
Ans: Complementary: Two angles are said to be complementary if the sum of their measures is 90o.
Supplementary: Two angles are said to be supplementary if the sum of their measures is 180o.
(i) 65°+ 115° = 180° [supplementary angles]
(ii) 63°+ 27° = 90° [Complementary angles]
(iii) 112o+ 68° =180° [supplementary angles]
(iv) 130°+ 50° = 180° [supplementary angles]
(v) 450 + 450 = 900 [Complementary angles]
(vi) 80°+10° =90° [Complementary angles]
Q.4. Find the angle which is equal to its complement.
Ans: Let the measure of the required angle = x.
We know that, sum of measures of complementary angle pair = 90o.
Then,
∴ x + x = 90o
⟹ 2x = 90o
⟹ $x=\frac{{{90}^{0}}}{2}$
⟹ x = 45o
Hence, 45o is equal to its complement.
Q.5. Find the angle which is equal to its supplement.
Ans: Let the measure of the required angle = x.
We know that, sum of measures of supplementary angle pair = 180o.
Then,
∴ x + x = 180o
⟹ 2x = 180o
⟹ $x=\frac{{{180}^{0}}}{2}$
⟹ x = 90o
Hence, 90o is equal to its supplement.
Q.6. In the given figure, ∠1 and ∠2 are supplementary angles. If ∠1 is decreased, what changes should take place in ∠2 so that both the angles still remain supplementary.
Ans: According to question, ∠1 and ∠2 are supplementary angles.
If ∠1 is decreased, then ∠2 will increase by the same value. So, that both the angles still remain supplementary.
Q.7. Can two angles be supplementary if both of them are:
(i) acute? (ii) obtuse? (iii) right?
Ans: (i) Acute: No, Because, their sum will be always less than 90o.
(ii) Obtuse: No, Because, their sum will be always more than 180o.
(iii) Right: Yes. Because, their sum will be always 180o.
∴ 90o + 90o = 180
Q.8. An angle is greater than 45º. Is its complementary angle greater than 45º or equal to 45º or less than 45º?
Ans: Let us assume the complementary angles be x and y,
We know that, sum of measures of complementary angles are 90o.
Then,
⟹ x + y = 90o
According to question, x > 45o
Adding y on both the sides,
⟹ x + y > 45o + y
⟹ 90o > 45o + y
⟹ 90o – 45o > y
⟹ y < 45o
Hence, its complementary angle is less than 45o.
Q.9. In the adjoining figure:
(i) Is ∠1 adjacent to ∠2?
(ii) Is ∠AOC adjacent to ∠AOE?
(iii) Do ∠COE and ∠EOD form a linear pair?
(iv) Are ∠BOD and ∠DOA supplementary?
(v) Is ∠1 vertically opposite to ∠4?
(vi) What is the vertically opposite angle of ∠5?
Ans: (i) Is ∠1 adjacent to ∠2?
Yes, as ∠1 and ∠2 having a common vertex i.e. O and a common arm OC. Their non-common arms OA and OE are on both the side of common arm.
(ii) Is ∠AOC adjacent to ∠AOE?
No, since they are having a common vertex O and common arm OA.
But, they have no non-common arms on both the side of the common arm.
(iii) Do ∠COE and ∠EOD form a linear pair?
Yes, they form linear pair.
(iv) Are ∠BOD and ∠DOA supplementary?
Yes, they are supplementary.
(v) Is ∠1 vertically opposite to ∠4?
Yes, they are vertically opposite angles.
(vi) What is the vertically opposite angle of ∠5?
Vertically opposite angles of ∠5 is ∠COB.
Q.10. Indicate which pairs of angles are: (i) Vertically opposite angles. (ii) Linear pairs.
Ans: (i) Vertically opposite angles: ∠1 and ∠4, ∠5 and ∠2 + ∠3 are vertically opposite angles. Because these two angles are formed by the intersection of two straight lines.
(ii) Linear pairs: ∠1 and ∠5, ∠5 and ∠4 as these are having a common vertex and also having non-common arms opposite to each other.
Q.11. In the following figure, is ∠1 adjacent to ∠2? Give reasons.
Ans: ∠1 and ∠2 are not adjacent angles. Because, they are not lie on the same vertex.
Q.12. Find the values of the angles x, y, and z in each of the following:
Ans:
(i) ∠x = 55o [Vertically opposite angles]
⟹ ∠x + ∠y = 180o [Linear pair]
⟹ 55o + ∠y = 180o
⟹ ∠y = 180o – 55o
⟹ ∠y = 125o
Then, ∠y = ∠z [Vertically opposite angles]
∴ ∠z = 125o
Thus, ∠x = 55o, ∠y = 125o, and ∠z = 125o.
(ii) ∠z = 40o [Vertically opposite angles]
∠y + ∠z = 180o [Linear pair]
⟹ ∠y + 40o = 180o
⟹ ∠y = 180o – 40o
⟹ ∠y = 140o
Then, 400 + ∠x + 250 = 180o [Angles on straight line]
⟹ 650 + ∠x = 180o
⟹ ∠x = 180o – 650
∴ ∠x = 115o
Thus, ∠x = 115o, ∠y = 140o, and ∠z = 40o.
Q.13. Fill in the blanks:
(i) If two angles are complementary, then the sum of their measures is _______.
(ii) If two angles are supplementary, then the sum of their measures is ______.
(iii) Two angles forming a linear pair are _______________.
(iv) If two adjacent angles are supplementary, they form a ___________.
(v) If two lines intersect at a point, then the vertically opposite angles are always _____________.
(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are __________.
Ans: (i) 90o (ii) 180o (iii) Supplementary (iv) linear pair (v) equal (vi) Obtuse angles
Q.14. In the adjoining figure, name the following pairs of angles.
(i) Obtuse vertically opposite angles
(ii) Adjacent complementary angles
(iii) Equal supplementary angles
(iv) Unequal supplementary angles
(v) Adjacent angles that do not form a linear pair
Ans:
(i) Obtuse vertically opposite angles
Obtuse vertically opposite angles means greater than 900 and equal. So, ∠AOD and ∠BOC are obtuse vertically opposite angles.
(ii) Adjacent complementary angles
Adjacent complementary angles means angles have common vertex, common arm,
non-common arms are on either side of common arm and sum of angles is 900.So, ∠EOA and ∠AOB are adjacent complementary angles.
(iii) Equal supplementary angles
Equal supplementary angles means sum of angles is 180° and supplement angles are
equal.so, ∠EOB and EOD are the equal supplementary angles.
(iv) Unequal supplementary angles
Unequal supplementary angles means sum of angles is 180° and supplement angles
are unequal. So, ∠EOA and ∠EOC are the unequal supplementary angles in the given figure.
(v) Adjacent angles that do not form a linear pair
Adjacent angles that do not form a linear pair mean, angles have common ray but the
angles in a linear pair are not supplementary. So, ∠AOB and ∠AOE, ∠AOE and ∠EOD, ∠EOD and ∠COD are the adjacent angles that do not form a linear pair in the given figure.