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) 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.
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.
(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?
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°