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

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.
It is an activity. Please do it yourself.

NCERT In-text Question Page No. 95
Question 1.
Which pairs of following angles are complementary?

(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°
(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.
∴ 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:

(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°
(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.
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’.

(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

(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.

(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

∠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.

NCERT In-text Question Page No. 104
Question 1.
Find examples from your surrounding where lines intersect at right angles.

Question 2.
Find the measure of the angles made by the intersecting lines at the vertices of an equilateral triangle.
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.
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?
No.

NCERT In-text Question Page No. 105
Question 1.
Suppose two lines are given. How many transversals can you draw for these lines?
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?
As shown in the adjoining figure, there are 3 distinct points of intersection.

Question 3.
Try to identify a few transversals in your surroundings.

NCERT In-text Question Page No. 106
Question 1.
Name the pairs of angles in each figure:

(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) 11 , 12 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.

(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.
(11 and 12 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?

(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°

error: Content is protected !!