### NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1

**Ex 5.1 Class 7 Maths Question 1.**

**Find the complement of each of the following angles:**

**Solution:**

(i) Complement of 20° = 90° – 20° = 70°

(ii) Complement of 63° = 90° – 63° = 27°

(iii) Complement of 57° = 90° – 57° = 33°

**Ex 5.1 Class 7 Maths Question 2.**

**Find the supplement of each of the following angles:**

**Solution:**

(i) Supplement of 105° = 180° – 105° = 75°

(ii) Supplement of 87° = 180° – 87° = 93°

(iii) Supplement of 154° = 180° – 154° = 26°

**Ex 5.1 Class 7 Maths Question 3.**

**Identify which of the following pairs of angles are complementary and which are supplementary?**

**(i) 65°, 115°**

**(ii) 63°, 27°**

**(iii) 112°, 68°**

**(iv) 130°, 50°**

**(v) 45°, 45°**

**(vi) 80°, 10°**

**Solution:**

(i) 65° (+) 115° = 180°

They are supplementary angles.

(ii) 63° (+) 27° = 90°

They are complementary angles.

(iii) 112° (+) 68° = 180°

They are supplementary angles.

(iv) 130° (+) 50° = 180°

They are supplementary angles.

(v) 45° (+) 45° = 90°

They are complementary angles.

(vi) 80° (+) 10° = 90°

They are complementary angles.

**Ex 5.1 Class 7 Maths Question 4.**

**Find the angle which equal to its complement.**

**Solution:**

Let the required angle be x°.

its complement = (90 – x)°

Now, re = 90 – x ⇒ x + x = 90

⇒ 2x = 90 ∴ x = 90/2 = 45°

Thus the required angles are 45°.

**Ex 5.1 Class 7 Maths Question 5.**

**Find the angle which is equal to its supplement.**

**Solution:**

Let the required angle be x°.

∴ it supplement = (180 – x)°

Now, x = 180 – x

⇒ x + x = 180

⇒ 2x = 180°

∴ x = 180°/2 =90°

Thus, the required angle is 90°.

**Ex 5.1 Class 7 Maths Question 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.**

**Solution:**

∠1 + ∠2 = 180° (given)

If ∠1 is decreased by some degrees, then ∠2 will also be increased by the same degree so that the two angles still remain supplementary.

**Ex 5.1 Class 7 Maths Question 7.**

**Can two angles be supplementary if both of them are:**

**(i) acute?**

**(ii) obtuse?**

**(iii) right?**

**Solution:**

(ii) Since, acute angle < 90°

∴ Acute angle + acute angle < 90° + 90° < 180° Thus, the two acute angles cannot be supplementary angles. (ii) Since, obtuse angle > 90°

∴ Obtuse angle + obtuse angle > 90° + 90° > 180°

Thus, the two obtuse angles cannot be supplementary angles.

(iii) Since, right angle = 90°

∴ right angle + right angle = 90° + 90° = 180°

Thus, two right angles are supplementary angles.

**Ex 5.1 Class 7 Maths Question 8.**

**An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45 °?**

**Solution:**

Given angle is greater than 45°

Let the given angle be x°.

∴ x > 45

Complement of x° = 90° – x° < 45° [ ∵ x > 45°]

Thus the required angle is less than 45°.

**Ex 5.1 Class 7 Maths Question 9.**

**In the following 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 angle to ∠4?**

**(vi) What is the vertically opposite angle of ∠5?**

**Solution:**

(i) Yes, ∠1 and ∠2 are adjacent angles.

(ii) No, ∠AOC is not adjacent to ∠AOE. [ ∵ OC and OE do not lie on either side of common arm OA] .

(iii) Yes, ∠COE and ∠EOD form a linear pair of angles.

(iv) Yes, ∠BOD and ∠DOA are supplementary. [∵ ∠BOD + ∠DOA = 180°]

(v) Yes, ∠1 is vertically opposite to ∠4.

(vi) Vertically opposite angle of ∠5 is ∠2 + ∠3 i.e. ∠BOC.

**Ex 5.1 Class 7 Maths Question 10.**

**Indicate which pairs of angles are:**

**(i) Vertically opposite angles**

**(ii) Linear pairs**

**Solution:**

(i) Vertically opposite angles are ∠1 and ∠4, ∠5 and (∠2 + ∠3)

(ii) Linear pairs are

∠1 and ∠5, ∠5 and ∠4

**Ex 5.1 Class 7 Maths Question 11.**

**In the following figure, is ∠1 adjacent to ∠2? Give reasons.**

**Solution:**

No, ∠1 and∠2 are not adjacent angles.

Reasons:

(i) ∠1 + ∠2 ≠ 180°

(ii) They have no common vertex.

**Ex 5.1 Class 7 Maths Question 12.**

**Find the values of the angles x, y and z in each of the following:**

**Solution:**

From Fig. 1. we have

∠x = ∠55° (Vertically opposite angles)

∠x + ∠y = 180° (Adjacent angles)

55° + ∠y = 180° (Linear pair angles)

∴ ∠y = 180° – 55° = 125°

∠y = ∠z (Vertically opposite angles)

125° = ∠z

Hence, ∠x = 55°, ∠y = 125° and ∠z = 125°

(ii) 25° + x + 40° = 180° (Sum of adjacent angles on straight line)

65° + x = 180°

∴ x = 180° – 65° = 115°

40° + y = 180° (Linear pairs)

∴ y = 180° – 40° = 140°

y + z = 180° (Linear pairs)

140° + z = 180°

∴ z = 180° – 140° = 40°

Hence, x – 115°, y = 140° and z – 40°

**Ex 5.1 Class 7 Maths Question 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 ______ .**

**Solution:**

(i) 90°

(ii) 180°

(iii) Supplementary

(iv) Linear pair

(v) Equal

(vi) Obtuse angle

**Ex 5.1 Class 7 Maths Question 14.**

**In the given 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 but do not form a linear pair.**

**Solution:**

(i) ∠BOC and ∠AOD are obtuse vertically opposite angles.

(ii) ∠AOB and ∠AOE are adjacent complementary angles.

(iii) ∠EOB and ∠EOD are equal supplementary angles.

(iv) ∠EOA and ∠EOC are unequal supplementary angles.

(v) ∠AOB and ∠AOE, ∠AOE and ∠EOD, ∠EOD and ∠COD are adjacent angles but do not form a linear pair.