Gujarat BoardĀ 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 20Ā° = 90Ā° – 20Ā° = 70Ā°

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

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

Question 2.

Find the supplement of each of the following angles:

Solution:

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

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

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

Question 3.

Identify which of the following pairs of angles are complementary and which are supplementary.

(i) 65Ā°, 115Ā°

(ii) 63Ā°, 27Ā°

(iii) 112Ā°, 68Ā°

(iv) 130Ā°, 50Ā°

(v) 45Ā°, 45Ā°

(vi) 80Ā°, 10Ā°

Solution:

(i) āµ 65Ā° + 115Ā° = 180Ā°

ā“ 65Ā° and 115Ā° are supplementary angles.

(ii) āµ 63Ā° + 27Ā° = 90Ā°

ā“ 63Ā° and 27Ā° are complementary angles.

(iii) āµ 112Ā° + 68Ā° = 180Ā°

ā“ 112Ā° and 68Ā° are supplementary angles.

(iv) āµ 130Ā° + 50Ā° = 180Ā°

ā“ 130Ā° and 50Ā° are supplementary angles

(v) āµ 45Ā° + 45Ā° = 90Ā°

ā“ 45Ā° and 45Ā° are complementary angles.

(vi) āµ 80Ā° + 10Ā° = 90Ā°

ā“ 80Ā° and 10Ā° are complementary angles.

Question 4.

Find the angle which is equal to its complement.

Solution:

Let the required angle be x.

āµ It is equal to its complement,

ā“ x = 90Ā° – x

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

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

or 2x = 90Ā°

Dividing both sides by 2, we have

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

Thus, 45Ā° 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 = (180Ā° – m)

āµ m is equal to its supplement.

ā“ m = 180Ā° – m

or m + m = 180Ā°

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

or 2m = 180Ā°

Dividing both sides by 2, we have

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

Thus, 90Ā° is equal to its supplement.

Question 6.

In the given figure, ā 1 and ā 2 are supplementary angles. If ā 1 is decreased, what changes should take place in ā 2 so that both the angles still remain supplementary.

Solution:

In case ā 1 is decreased, the same amount of degree measure is added to ā 2, i.e. ā 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) āµ Sum of two acute angles is always less than 180Ā°.

ā“ Two acute angles cannot be supplementary.

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

ā“ Two obtuse angles cannot be supplementary.

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

ā“ Two right angles are supplementary.

Question 8.

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

Solution:

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

Question 9.

In the adjoining figure:

(i) Is ā 1 adjacent to ā 2?

(ii) Is ā AOC adjacent to ā AOE?

(iii) Do ā COE and ā EOD form a linear pair?

(iv) Are ā BOD and ā DOA supplementary?

(v) Is ā 1 vertically opposite to ā 4?

(vi) Which is the vertically opposite angle of ā 5?

Solution:

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

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

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

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

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

(vi) The vertically opposite Wangle of ā 5 is ā BOC (or ā 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:

ā 1 and ā 4

ā 5 and (ā 2 + ā 3)

(ii) Linear pairs:

ā 4 and ā 5 form a linear pair.

ā 1 and ā 5 form a linear pair.

ā 1 and (ā 3 + ā 2) form a linear pair.

ā 4 and (ā 3 + ā 2) form a linear pair.

Question 11.

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

Solution:

No, ā 1 and ā 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 55Ā° are vertically opposite angles

x = 55Ā°

Again, 55Ā° + y = 180Ā° [Linear pair]

or y = 180Ā° – 55Ā°

or y = 125Ā°

Since z and y are vertically opposite angles,

ā“ z = 125Ā° [āµ y = 125Ā°]

Thus, x = 55Ā°, y = 125Ā°, z = 125Ā°

(ii) Since 40Ā° and z are vertically opposite angles, ā“ z = 40Ā°

Again y and 40Ā° form a linear pair.

ā“ y + 40Ā° = 180Ā°

[Transposing 40Ā° to R.H.S.]

or y = 180Ā° – 40Ā°

or y = 140Ā°

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

ā“ (x + 25Ā°) = y = 140Ā° [āµ y = 140Ā°]

or x = 140Ā° – 25Ā°

[Transposing 25Ā° to R.H.S.]

or x = 115Ā°

Thus, x = 115Ā°, y = 140Ā° and z = 40Ā°

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) 90Ā°

(ii) 180Ā°

(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) ā BOC and ā AOD are obtuse vertically opposite angles.

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

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

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

(v) (a) ā BOA and ā AOE

(b) ā AOE and ā EOD

(c) ā EOD and ā COD