Gujarat Board GSEB Textbook Solutions Class 7 Maths Chapter 5 Lines and Angles Ex 5.1 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 7 Maths Chapter 5 Lines and Angles Ex 5.1

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°

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°

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°

∴ 65° and 115° are supplementary angles.

(ii) ∵ 63° + 27° = 90°

∴ 63° and 27° are complementary angles.

(iii) ∵ 112° + 68° = 180°

∴ 112° and 68° are supplementary angles.

(iv) ∵ 130° + 50° = 180°

∴ 130° and 50° are supplementary angles

(v) ∵ 45° + 45° = 90°

∴ 45° and 45° are complementary angles.

(vi) ∵ 80° + 10° = 90°

∴ 80° and 10° are complementary angles.

Question 4.

Find the angle which is equal to its complement.

Solution:

Let the required angle be x.

∵ It is equal to its complement,

∴ x = 90° – x

[∵ (90° – x) is complement of x] or x + x = 90°

[Transposing x from R.H.S. to L.H.S.]

or 2x = 90°

Dividing both sides by 2, we have

\(\frac { 2x }{ 2 }\) = \(\frac { 90° }{ 2 }\) or x = 45°

Thus, 45° is equal to its complement.

Question 5.

Find the angle which is equal to its supplement.

Solution:

Let the required angle be m and supplement of m = (180° – m)

∵ m is equal to its supplement.

∴ m = 180° – m

or m + m = 180°

[Transposing m from R.H.S. to L.H.S.]

or 2m = 180°

Dividing both sides by 2, we have

\(\frac { 2m }{ 2 }\) = \(\frac { 180° }{ 2 }\) or m = 90°

Thus, 90° is equal to its supplement.

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:

In case ∠1 is decreased, the same amount of degree measure is added to ∠2, i.e. ∠2 be increased by same amount of degree measure.

Question 7.

Can two angles be supplementary if both of them are:

(i) acute?

(ii) obtuse

(iii) right?

Solution:

(i) ∵ Sum of two acute angles is always less than 180°.

∴ Two acute angles cannot be supplementary.

(ii) ∵ Sum of two obtuse angles is always more than 180°.

∴ Two obtuse angles cannot be supplementary.

(iii) ∵ Sum of two right angles = 180°.

∴ Two right angles are supplementary.

Question 8.

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

Solution:

Complement of an angle (greater than 45°) is less than 45°.

Question 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) Which is the vertically opposite angle of ∠5?

Solution:

(i) Yes, ∠1 and ∠2 are adjacent angles. Yes because both the angles have common arm OC and common vertex O.

(ii) No, ∠AOC is not adjacent to ∠AOE, because ∠AOC is part of ∠AOE.

(iii) Yes, ∠COE and ∠EOD form a linear pair, because \(\overset { \longleftrightarrow }{ COD }\) is a straight line.

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

(v) Yes, because AB and CD are straight lines.

(vi) The vertically opposite Wangle of ∠5 is ∠BOC (or ∠COB).

Question 10.

Indicate which pairs of angles are:

(i) Vertically opposite angles.

(ii) Linear pairs.

Solution:

(i) Vertically opposite angles:

In the figure, following pairs are vertically opposite angles:

∠1 and ∠4

∠5 and (∠2 + ∠3)

(ii) Linear pairs:

∠4 and ∠5 form a linear pair.

∠1 and ∠5 form a linear pair.

∠1 and (∠3 + ∠2) form a linear pair.

∠4 and (∠3 + ∠2) form a linear pair.

Question 11.

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

Solution:

No, ∠1 and ∠2 are not adjacent angles because they do not have a common vertex.

Question 12.

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

Solution:

(i) Since x and 55° are vertically opposite angles

x = 55°

Again, 55° + y = 180° [Linear pair]

or y = 180° – 55°

or y = 125°

Since z and y are vertically opposite angles,

∴ z = 125° [∵ y = 125°]

Thus, x = 55°, y = 125°, z = 125°

(ii) Since 40° and z are vertically opposite angles, ∴ z = 40°

Again y and 40° form a linear pair.

∴ y + 40° = 180°

[Transposing 40° to R.H.S.]

or y = 180° – 40°

or y = 140°

∵ y and (x + 25°) are vertically opposite angles

∴ (x + 25°) = y = 140° [∵ y = 140°]

or x = 140° – 25°

[Transposing 25° to R.H.S.]

or x = 115°

Thus, x = 115°, y = 140° and z = 40°

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 angles.

Question 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.

Solution:

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

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

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

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

(v) (a) ∠BOA and ∠AOE

(b) ∠AOE and ∠EOD

(c) ∠EOD and ∠COD