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

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) āµ 65Ā° + 115Ā° = 180Ā°
ā“ 65Ā° and 115Ā° are supplementary angles.

(ii) āµ 63Ā° + 27Ā° = 90Ā°
ā“ 63Ā° and 27Ā° are complementary angles.

(iii) āµ 112Ā° + 68Ā° = 180Ā°
ā“ 112Ā° and 68Ā° are supplementary angles.

(iv) āµ 130Ā° + 50Ā° = 180Ā°
ā“ 130Ā° and 50Ā° are supplementary angles

(v) āµ 45Ā° + 45Ā° = 90Ā°
ā“ 45Ā° and 45Ā° are complementary angles.

(vi) āµ 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.
āµ It is equal to its complement,
ā“ x = 90Ā° – x
[āµ (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)
āµ 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) āµ Sum of two acute angles is always less than 180Ā°.
ā“ Two acute angles cannot be supplementary.

(ii) āµ Sum of two obtuse angles is always more than 180Ā°.
ā“ Two obtuse angles cannot be supplementary.

(iii) āµ 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.
(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° [āµ 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°
āµ y and (x + 25Ā°) are vertically opposite angles
ā“ (x + 25Ā°) = y = 140Ā° [āµ 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.