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

**NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Exercise 5.1**

Ex 5.1 Class 7 Maths Question 1.

Find the complement of each of the following angles:

Solution:

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

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

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

Ex 5.1 Class 7 MathsÂ Question 2.

Find the supplement of each of the following angles:

Solution:

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

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

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

Ex 5.1 Class 7 MathsÂ Question 3.

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

(i) 65Â°, 115Â°

(ii) 63Â°, 27Â°

(iii) 112Â°, 68Â°

(iv) 130Â°, 50Â°

(v) 45Â°, 45Â°

(vi) 80Â°, 10Â°

Solution:

(i) 65Â° (+) 115Â° = 180Â°

They are supplementary angles.

(ii) 63Â° (+) 27Â° = 90Â°

They are complementary angles.

(iii) 112Â° (+) 68Â° = 180Â°

They are supplementary angles.

(iv) 130Â° (+) 50Â° = 180Â°

They are supplementary angles.

(v) 45Â° (+) 45Â° = 90Â°

They are complementary angles.

(vi) 80Â° (+) 10Â° = 90Â°

They are complementary angles.

Ex 5.1 Class 7 MathsÂ Question 4.

Find the angle which equal to its complement.

Solution:

Let the required angle be xÂ°.

its complement = (90 – x)Â°

Now, re = 90 – x â‡’ x + x = 90

â‡’ 2x = 90 âˆ´ x = \(\frac{90}{2}\) = 45Â°

Thus the required angles are 45Â°.

Ex 5.1 Class 7 MathsÂ Question 5.

Find the angle which is equal to its supplement.

Solution:

Let the required angle be xÂ°.

âˆ´ it supplement = (180 – x)Â°

Now, x = 180 – x

â‡’ x + x = 180

â‡’ 2x = 180Â°

âˆ´ \(x=\frac{180^{\circ}}{2}=90^{\circ}\)

Thus, the required angle is 90Â°.

Ex 5.1 Class 7 MathsÂ Question 6.

In the given figure, âˆ 1 and âˆ 2 are supplementary angles.

If âˆ 1 is decreased, what changes should take place inâˆ 2 so that both the angles still remain supplementary.

Solution:

âˆ 1 + âˆ 2 = 180Â° (given)

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

Ex 5.1 Class 7 MathsÂ Question 7.

Can two angles be supplementary if both of them are:

(i) acute?

(ii) obtuse?

(iii) right?

(ii) Since, acute angle < 90Â°

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

âˆ´ Obtuse angle + obtuse angle > 90Â° + 90Â° > 180Â°

Thus, the two obtuse angles cannot be supplementary angles.

(iii) Since, right angle = 90Â°

âˆ´ right angle + right angle = 90Â° + 90Â° = 180Â°

Thus, two right angles are supplementary angles.

Ex 5.1 Class 7 MathsÂ Question 8.

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

Solution:

Given angle is greater than 45Â°

Let the given angle be xÂ°.

âˆ´ x > 45

Complement of xÂ° = 90Â° – xÂ° < 45Â° [ âˆµ x > 45Â°]

Thus the required angle is less than 45Â°.

Ex 5.1 Class 7 MathsÂ Question 9.

In the following figure:

(i) Is âˆ 1 adjacent to âˆ 2?

(ii) Is âˆ AOC adjacent toâˆ AOE?

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

(iv) Are âˆ BOD and âˆ DOA supplementary?

(v) Is âˆ 1 vertically opposite angle to âˆ 4?

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

Solution:

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

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

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

(iv) Yes, âˆ BOD and âˆ DOA are supplementary. [âˆµ âˆ BOD + âˆ DOA = 180Â°]

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

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

Ex 5.1 Class 7 MathsÂ Question 10.

Indicate which pairs of angles are:

(i) Vertically opposite angles

(ii) Linear pairs

Solution:

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

(ii) Linear pairs are

âˆ 1 and âˆ 5, âˆ 5 and âˆ 4

Ex 5.1 Class 7 MathsÂ Question 11.

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

Solution:

No, âˆ 1 andâˆ 2 are not adjacent angles.

Reasons:

(i) âˆ 1 + âˆ 2 â‰ 180Â°

(ii) They have no common vertex.

Ex 5.1 Class 7 MathsÂ Question 12.

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

Solution:

From Fig. 1. we have

âˆ x = âˆ 55Â° (Vertically opposite angles)

âˆ x + âˆ y = 180Â° (Adjacent angles)

55Â° + âˆ y = 180Â° (Linear pair angles)

âˆ´ âˆ y = 180Â° – 55Â° = 125Â°

âˆ y = âˆ z (Vertically opposite angles)

125Â° = âˆ z

Hence, âˆ x = 55Â°, âˆ y = 125Â° and âˆ z = 125Â°

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

65Â° + x = 180Â°

âˆ´ x = 180Â° – 65Â° = 115Â°

40Â° + y = 180Â° (Linear pairs)

âˆ´ y = 180Â° – 40Â° = 140Â°

y + z = 180Â° (Linear pairs)

140Â° + z = 180Â°

âˆ´ z = 180Â° – 140Â° = 40Â°

Hence, x – 115Â°, y = 140Â° and z – 40Â°

Ex 5.1 Class 7 MathsÂ 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) 90Â°

(ii) 180Â°

(iii) Supplementary

(iv) Linear pair

(v) Equal

(vi) Obtuse angle

Ex 5.1 Class 7 MathsÂ 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) âˆ BOC and âˆ AOD are obtuse vertically opposite angles.

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

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

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

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

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