These NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles InText Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles InText Questions

NCERT In-text Question Page No. 94

Question 1.

List ten figures around you and identify the acute, obtuse and right angles found in them.

Answer:

It is an activity. Please do it yourself.

NCERT In-text Question Page No. 95

Question 1.

Which pairs of following angles are complementary?

Answer:

(i) Since 70° + 20° = 90°

∴ Angles 70 and 20 are complementary.

(ii) ∵ 75° + 25° = 100° and 100° ≠ 90°

Angles 75° and 25° are not complementary.

(iii) ∵ 48° + 52° = 100° and 100° = 90°

The angles 48° and 52° are not complementary.

(iv) ∵ 35° + 55° = 90°

∵ The angles 35 and 55 are complementary.

Question 2.

What is the measure of the complement of each of the following angles?

(i) 45°

(ii) 65°

(iii) 41°

(iv) 54°

Answer:

(i) Let the complement of 45° be x

∴ x + 45° = 90°

x = 90° – 45°

= 45°

The complement of 45° is 45°.

(ii) Let the complement of 65° be p

∴ p + 65° =90°

p = 90° – 65°

= 25°

The complement of 65° is 25°.

(iii) Let the complement of 41° be m

∴ m + 41° = 90°

m = 90° – 41°

= 49°

The complement of 41° is 49°.

(iv) Let the complement of 54° be y

∴ y + 54° = 90°

∴ y = 90° – 54°

= 36°

The complement of 54° is 36°.

Question 3.

The difference in the measures of two complementary angles is 12°. Find the measures of the angles.

Answer:

∴ Let one of the angle be x

∴ The difference =12°

∴ The other angle = x + 12°

Sum of the measures of two angles = 90°

Since x and x + 12° are complementary angles

∴ x + x + 12° = 90

2x + 12 = 90°

Transpose 12 to R.H.S

2x = 90 – 12

2x = 78°

Dividing both sides by 2, we get

\(\frac{2 x}{2}=\frac{78}{2}\)

x = 39°

∴ The other angle = 39° +12°

= 51°

The measures of the angle are 39° and 51°.

NCERT In-text Question Page No. 96 & 97

Question 1.

Find the pairs of supplementary angles in following figures:

Answer:

(i) 110° and 50° are not a pair of

supplementary angles as 110° + 50° = 160° ≠ 180°

(ii) 105° and 65° are not a pair of supplementary angles as

105°+ 65° = 170° ≠ 180°

(iii) 50° and 130° are a pair of supplementary angles as

50° + 130° = 180°

(iv) 45° and 45° are not a pair of supplementary angles as

45°+ 45° = 90° ≠ 180°

Question 2.

What will be the measure of the supplement of each one of the following angles?

(i) 100°

(ii) 90°

(iii) 55°

(iv) 125°

Answer:

(i) Let the supplement of 100° be x.

∴ 100°+ x = 180°

or x = 180° – 100° = 80°

∴ The measure of the supplement of 100° is 80°.

(ii) Let the supplement of 90° be x.

∴ x + 90° = 180°

or x = 180°- 90°= 90°

∴ The measure of the supplement of 90° is 90°.

(iii) Let the supplement of 55° be m.

∴ 55° + m = 180°

or m = 180° – 55°

or m = 125°

∴ The supplement of 55° is 125°.

(iv) Let the supplement of 125° be y.

∴ y + 125°= 180°

or y = 180° – 125°

or y = 55°

∴ The supplement of 125° is 55°.

Question 3.

Among two supplementary angles the measure of the larger angle is 44° more than the measure of the smaller. Find their measures.

Answer:

Let the smaller angle be x

∴ The measure of the larger angle = (x + 44°)

Since the two angles are supplementary,

x + (x + 44°) = 180°

2x + 44° = 180°

2x = 180° – 44°

2x = 136°

x = \(\frac{136}{2}\) = 68°

∴ The smaller angle = 68°

Larger angle= 68° + 44° =112°

So, the supplementary angles are 68° and 112°.

NCERT In-text Question Page No. 97 & 98

Question 1.

Are the angles marked 1 and 2 adjacent? If they are not adjacent, say, ‘why’.

Answer:

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

(ii) ∠1 and ∠2 are adjacent angles.

(iii) ∠1 and ∠2 are not adjacent angles because they have no common vertex.

(iv) No, ∠1 and ∠2 are not adjacent angles because ∠1 is a part of ∠2.

(v) Yes, ∠1 and ∠2 are adjacent angles.

Question 2.

In the given figure, are the following adjacent angles?

(a) ∠AOB and ∠BOC

(b) ∠BOD and ∠BOC

Justify your answer.

Answer:

(a) Yes, ∠AOB and ∠BOC are adjacent angles, because they have common vetex O and their non-common arms (OA and OC) are on either side of the common arm OB.

(b) No, because ∠BOC is a part of ∠BOD.

NCERT In-text Question Page No. 99

Question 1.

Check which of the following pairs of angles form a linear pair.

Answer:

(i) yes,

∵ 140° + 40° = 180°

∴ The given pair of angles forms a linear pair.

(ii) No.

∵ 60° + 90° = 150° and 150° ≠ 180°

∴ The given pair of angles does not form a linear pair.

(iii) No.

∵ 90° + 80° = 170° and 170° ≠ 180°

∴ The given pair of angles does not form a linear pair.

(iv) Yes.

∵ 115° + 65° = 180°

∴ The given pair of angles forms a linear pair.

NCERT In-text Question Page No. 101

Question 1.

In the given figure if ∠1 = 30°, find ∠2 and ∠3

Answer:

∠3 and ∠1 are vertically opposite angles.

.’. ∠3 = ∠1

Since ∠1 = 30°, So ∠3 = 30°

Again ∠3 and ∠2 form a linear pair

.’. ∠3 + ∠2 = 180°

30° + ∠2 = 180°

∠2 = 180° – 30°= 150°

Thus ∠2 = 150° and ∠3 = 30°

Question 2.

Give an example for vertically opposite angles in your surrounding.

Answer:

Please do it yourself.

NCERT In-text Question Page No. 104

Question 1.

Find examples from your surrounding where lines intersect at right angles.

Answer:

Please do it yourself.

Question 2.

Find the measure of the angles made by the intersecting lines at the vertices of an equilateral triangle.

Answer:

Points of intersection are A, B and C.

Measure of ∠A = 60°

Measure of ∠B = 60°

Measure of ∠C = 60°

Question 3.

Draw any rectangle and find the measures of angles at the four vertices made by the intersecting lines.

Answer:

Measure of ∠A = 90°

Measure of ∠B = 90°

Measure of ∠C = 90°

Measure of ∠D = 90°

Question 4.

If two lines intersect, do they always intersect at right angles?

Answer:

No.

NCERT In-text Question Page No. 105

Question 1.

Suppose two lines are given. How many transversals can you draw for these lines?

Answer:

We can draw an infinite number of transversals to two given lines.

Question 2.

If a line is a transversal to three lines, how many points of intersections are there?

Answer:

As shown in the adjoining figure, there are 3 distinct points of intersection.

Question 3.

Try to identify a few transversals in your surroundings.

Answer:

Please do it yourself.

NCERT In-text Question Page No. 106

Question 1.

Name the pairs of angles in each figure:

Answer:

(i) ∠1 and ∠2 are a pair of corresponding angles.

(ii) ∠3 and ∠4 are a pair of alternate interior angles.

(iii) ∠5 and ∠6 are a pair of interior angles on the same side of the transversal.

(iv) ∠7 and ∠8 are a pair of corresponding angles.

(v) ∠9 and Z10 are a pair of alternate interior angles.

(vi) ∠11 and ∠12 are linear pair of angles.

NCERT In-text Question Page No. 109

Question 1.

Find the missing values.

(i) Lines l || m; t is a transversal ∠x = ?

(ii) Lines a || b; c is a transversal ∠y = ?

(iii) 1_{1} , 1_{2} be two lines t is a transversal Is ∠1 = ∠2?

(iv) Lines l || m; t is a transversal ∠z =?

(v) Lines l || m; t is a transversal ∠x =?

(vi) Lines l || m, p || q; Find a, b, c, d.

Answer:

(i) x = 60°

(x and 60° are alternate interior angles)

(ii) y = 55°

[∴ y and 55° are alternate interior angles]

(iii) No, ∠1 and ∠2 are not equal.

(1_{1} and 1_{2} are not parallel).

(iv) 60° + z = 180°

[z and 60° are interior angles on the same side of the transversal]

z = 180° – 60° = 120°

(v) x = 120°

[x and 120° are corresponding angles]

(vi) a + 60° = 180°

(Interior angles on same side of transversal)

a = 180 – 60° = 120° a = b = 120°

(alternate exterior angles)

b + d = 180°(linear pair)

d + 120 = 180°

d = 180° – 120° = 60°

⇒ c = b = 120°

(Vertically opposite angles)

NCERT In-text Question Page No. 110

Question 1.

(i) Is l || m? Why?

(ii) Is 1 || m ? Why?

(iii) If || m, what is ∠x?

Answer:

(i) If a transversal intersects two given lines such that alternate angles are equal, then the given lines are parallel.

Since 50° = 50°(alternate angles)

∴ l || m

(ii) l || m as a pair of interior angles on the same side of the transversal are supplementary

Here

x + 130° = 180° (Linear Pair)

x = 50°

y = x = 50°

⇒ l || m (as alternate angles are equal)

(iii) l and m are parallel and t is a transversal

∴ The sum of interior angles on the same side of the transversal is 180°.

x + 70° = 180°

x = 180°- 70°

x = 110°