Q.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°

NCERT Solutions for Class 7 Maths Chapter 5 Lines And Angles

Answer :

(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.

Q.6 In the given figure,

If

NCERT Solutions for Class 7 Maths Chapter 5 Lines And Angles

Answer :

If

NCERT Solutions for Class 7 Maths Chapter 5 Lines And Angles

Answer :

(i) No, If two angles are acute, means less than 90°, the two angles cannot be supplementary. Because, their sum will be always less than 180° .

(ii) No. If two angles are obtuse, means more than 90°, the two angles cannot be supplementary. Because, their sum will be always more than 180°.

(iii) Yes. If two angles are right, means both measures 90°, then two angles can form a supplementary pair.

90° + 90° = 180°

Q.8 An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45 °?

NCERT Solutions for Class 7 Maths Chapter 5 Lines And Angles

Answer :

Given angle is greater than 45°

Let the given angle be x°.

So, x > 45

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

Thus the required angle is less than 45°.

Q.9 In the following figure:

(i) Is

(ii) Is

(iii) Do

(iv) Are

(v) Is

(vi) What is the vertically opposite angle of

NCERT Solutions for Class 7 Maths Chapter 5 Lines And Angles

Answer :

(i) Yes,

because it's one arm (OC) is common

(ii) No,

[ because OC and OE do not lie on either side of common arm OA] .

(iii) Yes,

(iv) Yes,

[Because

(v) Yes,

(vi) Vertically opposite angle of

NCERT Solutions for Class 7 Maths Chapter 5 Lines And Angles

Answer :

(i) Vertically opposite angles are angle1 and angle 4,

(ii) Linear pairs are

NCERT Solutions for Class 7 Maths Chapter 5 Lines And Angles

Answer :

No,

Reasons:

(i) They have no common vertex.

(ii)

NCERT Solutions for Class 7 Maths Chapter 5 Lines And Angles

Answer :

From Fig. 1. we have

55° +

So,

Hence,

From Fig. ii . we have

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

65° + x = 180°

So, x = 180° – 65° = 115°

40° + y = 180° (Linear pairs)

So, y = 180° – 40° = 140°

y + z = 180° (Linear pairs)

140° + z = 180°

So, z = 180° – 140° = 40°

Hence, x – 115°, y = 140° and z – 40°

Q.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 ______ .

NCERT Solutions for Class 7 Maths Chapter 5 Lines And Angles

Answer :

(i) If two angles are complementary, then the sum of their measures is _90°_ .

(ii) If two angles are supplementary, then the sum of their measures is _180°_ .

(iii) Two angles forming a linear pair are _suplimentry_ .

(iv) If two adjacent angles are supplementary, they form a _linear pair_.

(v) If two lines intersect at a point, then the vertically opposite angles are always _equal_ .

(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 _obtuse angle_ .

Q.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.

NCERT Solutions for Class 7 Maths Chapter 5 Lines And Angles

Answer :

(i)

(ii)

(iii)

(iv)

(v)

Q.1 State the property that is used in each of the following statements?

(i) If a

(ii) If

(iii) If

NCERT Solutions for Class 7 Maths Chapter 5 Lines And Angles

Answer :

(i) Given a

So,

(ii) Given:

So, a

(iii) Given:

So, a

Q.2 In the given figure, identify

(i) the pairs of corresponding angles.

(ii) the pairs of alternate interior angles.

(iii) the pairs of interior angles on the same side of the transversal.

NCERT Solutions for Class 7 Maths Chapter 5 Lines And Angles

Answer :

(i) The pair of corresponding angles are

(ii) The pairs of alternate interior angles are

(iii) The pairs of interior angles on the same side of the transversal are

NCERT Solutions for Class 7 Maths Chapter 5 Lines And Angles

Answer :

Thus,

NCERT Solutions for Class 7 Maths Chapter 5 Lines And Angles

Answer :

(i) Let the angle opposite to 110° be y.

Thus x= 70°

(ii)

Q.5 the given figure, the arms of two angles are parallel. If

(i)

(ii)

NCERT Solutions for Class 7 Maths Chapter 5 Lines And Angles

Answer :

Given

AB

BC

(i)

(ii)

NCERT Solutions for Class 7 Maths Chapter 5 Lines And Angles

Answer :

(i) Sum of interior angles on the same side of transversal
= 126° + 44° = 170°

(ii) Let angle opposite to 75° be x.

x = 75° [Vertically opposite angles]

= x + 75° = 75° + 75°

= 150°

(iii) Let the angle opposite to 57° be y.

= 57° + 123° = 180°

(iv) Let angle opposite to 72° be z.

[Sum of interior angles on the same side of transversal]

= z + 98° = 72° + 98°= 170°

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