RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions

Rajasthan Board RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions Textbook Exercise Questions and Answers.

Rajasthan Board RBSE Solutions for Class 7 Maths in Hindi Medium & English Medium are part of RBSE Solutions for Class 7. Students can also read RBSE Class 7 Maths Important Questions for exam preparation. Students can also go through RBSE Class 7 Maths Notes to understand and remember the concepts easily. Students can access the data handling class 7 extra questions with answers and get deep explanations provided by our experts.

RBSE Class 7 Maths Solutions Chapter 5 Lines and Angles Intext Questions

(Think, Discuss and Write: Page No: 95)

Question 1.
Can two acute angles be com¬plement to each other?
Answer:
Yes, because sum of measures of two acute angles can be 90°.

RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions

Question 2.
Can two obtuse angles be complement to each other?
Answer:
No, because sum of measures of two obtuse angles cannot be 90° as each obtuse angle is greater than 90°.

Question 3.
Can two right angles be complement to each other?
Answer:
No, because sum of measures of two right angles will be 180°.

RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions

(Try These Page No: 95)

Question 1.
Which pair of following angles are complementary?
(i)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions
Answer:
∵ 70° + 20° = 90°
∴ Pair of 70°, 20° is the pair of complementary angles.

(ii)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 2
Answer:
∵ 75° + 25° = 100°
∴ Pair of 75°, 25° is not the pair of complementary angles.

(iii)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 3
Answer:
∵ 48° + 52° = 100°
∴ Pair of 48°, 52° is not the pair of complementary angles.

(iv)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 4
Answer:
∵ 35° + 55° = 90°
∴ Pair of 35°, 55° is the pair of complementary angles.

RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions

Question 2.
What is the measure of the com-plement of each of the following angles?
(i) 45°
Answer:
Complementary angle of 45°
= 90° - 45° = 45°

(ii) 65°
Answer:
Complementary angle of 65°
= 90°- 65° = 25°

(iii) 41°
Answer:
Complementary angle of 41°
= 90°- 41° = 49°

(iv) 54°
Answer:
Complementary angle of 54°
= 90° - 54° = 36°

Question 3.
The difference in the measures of two complementary angles is 12°. Find the measures of the angles.
Answer:
Let the smaller angle be x.
∵ Their difference = 12°
∴ The other angle = x + 12°
Since, the sum of the measures of two complementary angles is 90°.
Therefore, x + 12° + x = 90°
⇒ 2x + 12° = 90°
⇒ 2x = 90° - 12°
⇒ 2x = 78°
⇒ x = \(\frac{78^{\circ}}{2}\)
⇒ x = 39°
∴ Smaller angle = 39°
Other angle = 39° + 12° = 51°

RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions

(Think, Discuss and Write: Page No: 96)

Question 1.
Can two obtuse angles be supplementary?
Answer:
No, because sum of measure of two obtuse angles will be more than 180°.

Question 2.
Can two acute angles be supplementary?
Answer:
No, because sum of measure of two acute angles will be less than 180°.

Question 3.
Can two right angles be supplementary?
Answer:
Yes, because sum of measure of two right angles will be 180°.

(Try These Page No:96 - 97)

Question 1.
Find the pairs of supplementary angles in:

(i)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 5
Answer:
∵ 110° + 50° = 160°
∴ Pair of 110° and 50° is not the pair of supplementary angles.

(ii)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 6
Answer:
∵ 105° + 65° = 170°
∴ Pair of. 105° and 65° is not the pair of supplementary angles.

(iii)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 7
Answer:
∵ 50° + 130° = 180°
∴ Pair of 50° and 130° is the pair of supplementary angles.

RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions

(iv)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 8
Answer:
∵ 45° + 45° = 90°
∴ Pair of 45° and 45° is not the pair of supplementary angles.

Question 2.
What will be the measure of the supplement of each one of the following angles?
(i) 100°
Answer:
Supplement of 100° = 180° - 100° = 80°

(ii) 90°
Answer:
Supplement of 90° = 180° - 90° = 90°

(iii) 55°
Answer:
Supplement of 55° = 180° - 55° = 125°

(iv) 125°
Answer:
Supplement angle of 125° = 180° - 125° = 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.
Then, measure of larger angle = x + 44°.
Since, the sum of the measures of two supplementary angles is 180°.
Therefore, x + 44° + x = 180°
⇒ 2x + 44° = 180°
⇒ 2x = 180° - 44°
⇒ 2x = 136°
⇒ x = \(\frac{136^{\circ}}{2}\)
⇒ x = 68°
∴ Smaller angle = 68°
Other angle = 68° + 44° = 112°

RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions

(Try These Page No: 97 - 98)

Question 1.
Are the angles marked 1 and 2 adjacent? If they are not adjacent, say, 'why'?
(i)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 9
Answer:
Yes, ∠1 and ∠2 are adjacent angles.

(ii)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 10
Answer:
Yes, ∠1 and ∠2 are adjacent angles.

(iii)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 11
Answer:
No, ∠1 and ∠2 are not adjacent angles because they have no common vertex.

(iv)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 12
Answer:
No, ∠1 and ∠2 are not adjacent angles because their non-common arms are not on either side of the common arm.

(v)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 13
Answer:
Yes, ∠1 and ∠2 are adjacent angles.

RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions

Question 2.
In the given figure, are the following adjacent angles.
(a) ∠AOB and ∠BOC
(b) ∠BOD and ∠BOC
Justify your answer.
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 14
Answer:
(a) Yes, ∠AOB and ∠BOC are.adjacent angles because they have common vertex O, a common arm OB and non-common arms OA and OC are on either side of common arm OB.
(b) No, because there non-common arms OC and OD are not on either side of common arm BO.

(Think, Discuss and Write: Page No: 98)

Question 1.
Can two adjacent angles be supplementary?
Answer:
Yes, two adjacent angles may be supplementary.

Question 2.
Can two adjacent angles be complementary?
Answer:
Yes, two adjacent angles may be complementary.

Question 3. Can two obtuse angles be adjacent angles?
Answer:
Yes, two obtuse angles may be adjacent angles.

Question 4.
Can an acute angle be adjacent to an obtuse angle?
Answer:
Yes, an acute angle and an obtuse angle may be adjacent angles.

(Think, Discuss and Write: Page No: 99)

Question 1.
Can two acute angles form a linear pair?
Answer:
No, because the measure of each acute angle is less than 90° so the sum of the measures of two acute angles is less than 180°.

Question 2.
Can two obtuse angles form a linear pair?
Answer:
No, because the measure of each obtuse angle is more than 90° so the sum of the measures of two obtuse angles is greater than 180°.

RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions

Question 3.
Can two right angles form a linear pair?
Answer:
Yes, because the sum of the measures of two right angles is 180°.

(Try These: Page No: 99)

Question 1.
Check, which of the following pairs of angles form a linear pair?
(i)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 15
Answer:
As the sum of linear pair of angles is 180°, then
∵ 140° + 40° = 180°
∴ The pair of angles 140°, 40° form a linear pair.

(ii)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 16
Answer:
As the sum of linear pair of angles is 180°, then
∵ 90° + 60° = 150°
∴ The pair of angles 60°, 60° do not form a linear pair.

(iii)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 17
Answer:
As the sum of linear pair of angles is 180°, then
∵ 90° + 80° = 170°
∴ The pair of angles 90° and 80° do not form a linear pair.

RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions

(iv)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 18
Answer:
As the sum of linear pair of angles is 180°, then
∵ 115° + 65° = 180°
∴ The pair of angles 115°, 65° form a linear pair.

(Try These Page No: 101)

Question 1.
In the given figure, if ∠1 = 30°, find ∠2 and ∠3.
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 19
Answer:
∵ ∠3 and ∠1 are vertically opposite angles.
∴ ∠3 = ∠1
∠3 = 30°
Again ∠3 + ∠2 form
∴ ∠3 + ∠2 = 180°
⇒ 30° + ∠2 = 180°
⇒ ∠2 = 180° - 30°
∴ ∠2 = 150°

Question 2.
Give an example for vertically opposite angles in your surroundings.
Answer:
English alphabet ‘X’ is an example of vertically opposite angles.

(Think, Discuss and Write: Page No: 104)

Question 1.
In fig. AC and BE intersect at P.
AC and BC intersect at C, AC and EC intersect at C.
Try to find another ten pairs of intersecting line segments.
Should any two lines or line segments necessarily intersect? Can you find two pair of non-intersecting line segments in the figure?
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 20
Can two lines intersect in more than one point? Think about it.
Answer:
Various pairs of intersecting lines are:
(a) BC and BE
(b) BP and BC
(c) BC and EC
(d) PC and EC
(e) BE and CE
(f) PE and CE
(g) BP and CP
(i) AP and BP
If any two lines or line segments are not parallel, then they necessarily intersect. In this figure, there is no pair of parallel lines (non-intersecting lines). Two intersecting lines cannot intersect in more than one point, they intersect in one and only one point.

(Try These Page No: 104)

Question 1.
Find examples from your surroundings where lines intersect at right angles.
Answer:
Crossing of the road, English alphabet L, intersection of edges of a cuboid, etc. are the examples where lines intersect at right angles.

RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions

Question 2.
Find the measures of the angles made by the intersecting lines at the vertices of an equilateral triangle.
Answer:
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 21
Let lines p, q and r intersects at points A, B and C.
Equilateral triangle so formed is ABC.
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:
Let lines p, q, r and s intersects at points A, B, C and D. Rectangle so formed is ABCD.
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 22
Measure of ∠A = 90°
Measure of ∠B = 90°
Measure of ∠C = 90°
Measure of ∠D = 90°

Question 4.
If two lines intersects, do they always intersect at right angles?
Answer:
No, if two lines intersects, they may or may not be intersects at right angles.

(Try These 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 for two lines.

RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions

Question 2.
If a line is a transversal to three lines, how many points of intersections are there?
Answer:
There are three distinct points of intersecting as shown in the figure where line p is the transversal to lines l, m and n.
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 23

Question 3.
Try to identify a few transversals in your surroundings.
Answer:
(i) A grill of a window.
(ii) A line drawn to intersect the lines of the ruled sheet of paper.

(Try These Page No: 106)

Question 1.
Name the pair of angles in each figures
(a)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 24
Answer:
∠1 and ∠2 are the pair of corresponding angles.

(b)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 25
Answer:
∠3 and ∠4 are the pair of alternate interior angles.

(c)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 26
Answer:
∠5 and ∠6 are the pair of interior angles on the same side of the transversal.

(d)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 27
Answer:
(d) ∠7 and ∠8 are the pair of corresponding angles.

(e)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 28
Answer:
∠9 and ∠10 are the pair of alternate interior angles.

(f)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 29
Answer:
∠11 and ∠12 are the linear pair of angles.

RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions

(Try These: Page No: 109)

(a)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 30
Lines l || m; t is a transversal ∠x = ?
Answer:
Lines l || m, x and 60° are the pair of alternate interior angles, they will be equal, x = 60°
∴ x = 60°

(b)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 31
Lines a || b; c is a transversal ∠y = ?
Answer:
Lines a || b, y and 55° are the pair of alternate interior angles, they will be equal.
y = 55°

(c)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 32
Lines l1, l2 be two lines. t is a transversal ∠1 = ∠2 ?
Answer:
(c) ∵ ∠1, ∠2 are the pair of alternate interior angles but lines M and l2 are not parallel.
∴ ∠1 ≠ ∠2

(d)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 33
Lines l || m; t is a transversal ∠z = ?
Answer:
Lines l || m, z and 60° are the pair of interior angles on the same side of the transversal, they are supplementary.
∴z + 60° = 180°
⇒ z = 180° - 60°
∴z = 120°

(e)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 34
Lines l || m; t is a transversal ∠x = ?
Answer:
Lines l || m and x, 120° are pair of corresponding angles and they are equal.
∴x = 120°

(f)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 35
Lines l || m, p || q; find a, b, c, d.
Answer:
∵ Lines p || q, a and 60° are pair of interior angles on the same side of the transversal, they are supplementary.
∴a + 60° = 180°
⇒ a = 180° - 60°
∴a = 120°
∵ Lines M || m and vertically opposite angles of a, and c are the pair of interior angles on the same side of the transversal.
∴a + e = 180°
⇒ 120° + c = 180°
⇒ c = 180° -120° '
∴c = 60°
Now, b and c are vertically opposite angles.
∴ b = 60°
Also, b + d = 180° (linear pair)
⇒ 60° + d = 180°
∴ d = 180° - 60° = 120°

RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions

(Try These: Page No: 110)

Question (a)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 36
Is l || m? Why?
Answer:
∵ Pair of alternate interior angle is equal.
∴ l || m

Question (b)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 37
Is l || m? Why?
Answer:
∵ Alternate interior angle of 50° is equal to 180° - 130° = 50°, i.e. alternate interior angles are equal.
∴ l || m

Question (a)
RBSE Solutions for Class 7 Maths Chapter 5 Lines and Angles Intext Questions 38
Is l || m? Why ∠x?
Answer:
∵ Lines l || m, x and 70°are the interior angles on the same side of the transversal.
∴ x + 70° = 180°
⇒ x = 180° - 70°
∴ x = 110° 

Bhagya
Last Updated on June 14, 2022, 11:57 a.m.
Published June 13, 2022