# RS Aggarwal Solutions Class 9 Maths Chapter 7 Lines and Angles (Updated For 2021-22) RS Aggarwal Solutions Class 9 Maths Chapter 7 Lines and Angles: Ace your Class 9 Maths exam with the RS Aggarwal Solutions Class 9 Maths. You can start studying the RS Aggarwal Solutions Class 9 Maths Chapter 7 Lines and Angles for scoring good marks. Subject matter experts have designed well-explained and easy to understand solutions that are credible too.

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RS Aggarwal Solutions Class 9 Maths Chapter 7 Lines and Angles

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### RS Aggarwal Solutions Class 9 Maths Chapter 7 Lines and Angles Ex 7.1

1: Define the following terms:

(i) Angle
When two rays originated from same point, then an angle is formed.

(ii) Interior of an angle
The area between two rays which is originated from same point, is called Interior of an angle.

(iii) Obtuse angle
An angle which is measured more than 900 but less than 1800 is called Obtuse angle.

(iv) Reflex angle
An angle which is measured more than 1800 but less than 3600 is called Reflex angle.

(v) Complementary angle
Two angle are said to be complementary if, the sum of both angles are 900 .

(vi) Supplementary angle
Two angle are said to be supplementary, if the sum of both angles are 1800.

2: Find the complement of each of the following angles:

(i) 550 (ii) 160 (iii) 900 (iv) 2/3 of a right angle

Complement of 550 = 900 – 550 = 350

Complement of 160 = 900 – 160= 740

Complement of 900 = 900 – 900 = 00

Complement of 2/3 of a right angle
= 900 – ( 900 × 2/3) = 900 – 600 =300

3: Find the supplementary of each of the following angles:

(i) 420      (ii) 900       (iii) 1240    (iv) 3/5 of a right angle

Supplementary of 420 = 1800 – 42=1380

Supplementary of 900 = 1800 – 90= 900

Supplementary of 1240 = 1800 –  124= 560

Supplementary of 3/5 of a right angle
= 1800 – ( 900 × 3/5) = 1800 – 540= 1260

4: Find the measure of an angle which is

(i) equal to its complement,
Let the angle is x0 , then
⇒ x0 = 900 – x0
⇒ 2x0 = 900
⇒ x0 = 450

Hence the angle is 450 which is equal to its complement.

(ii) equal to its supplement
Let the angle is x0 then
⇒ x0 = 1800 – x0
⇒ 2x0 = 1800
⇒ x0 = 900

Hence the angle is 900 which is equal to its supplement.

5: Find the measure of an angle which is 360 more than its complement.

Let the angle is x0 , then its complement angle will be 900 – x0
According to question,
⇒ x0 – 360 = 900 – x0
⇒ 2x0 = 900 + 360 = 1260
⇒ x0 = 630

Hence the angle is 630 .

6: Find the measure of an angle which is 300 less than its supplement.

Let the angle is x0, then its supplement angle will be 1800 – x0

According to question,
⇒ x0 +300 = 1800 – x0
⇒ 2x0 = 1800 – 300 = 1500
⇒ x0 = 750
Hence the angle is 750.

7: Find the angle which is four times its complement.

Let the angle is x0, then its complement angle will be 900 – x0
According to question,
⇒ x0 = 4(900 – x0 )
⇒ x0 = 3600 – 4x0
⇒ 5x0 = 3600
⇒ x0= 720

Hence the angle is 720

8: Find the angle which is five times its supplement.

Let the angle is x0, then its supplementary angle will be 1800 – x0
According to question,
⇒ x0 = 5(1800 – x0 )
⇒ x0 = 9000 – 5x0
⇒ 6x0 = 9000
⇒ x0 = 1500

Hence the angle is 1500 .

9: Find the angle whose supplement is four times its complement.

Let the angle is x0, then its supplement angle will be 1800 – x0
and complement will be 900 – x0

According to question,
⇒ (1800 – x0 ) = 4(900 – x0 )
⇒ 1800 – x0 = 3600 – 4x0
⇒ 4x0 – x0 = 3600 – 1800 = 1800
⇒ 3x0=1800
⇒ x0 = 600

10: Find the angle whose complement is one third of its supplement.

Let the angle is x0 , then its supplement angle will be 1800 – x0
and complement will be 900 – x0

According to question,
⇒ (900 – x0) = 1/3 (1800 – x0)
⇒2700 – 3x0= 1800 – x0
⇒ – 3x0 + x0 = 1800 – 2700 = –900
⇒ – 2x0 = – 900
⇒ x0 = 450

Hence the angle is 450 .

11: Two complementary angles are in the ratio 4 : 5. Find the angles.

Hence the angles are 400 and 500 .

12: Find the value of x for which the angles (2x – 5)0
and (x – 10)0 are complementary angles.

Since the given angle are complementary to each other, therefore sum of both angle will be 900

So, (2x – 5)0 + (x – 10)0 = 900
⇒ (3x – 15)0 = 900
⇒3x = 900 +150 = 1050
⇒ x0 = 350
Hence the angle is 350.

### RS Aggarwal Solutions Class 9 Maths Chapter 7 Lines and Angles Ex 7.2

1: In the adjoining figure, AOB is a straight line. Find the value of x.

Solution:

From figure,
⇒∠AOC+∠COB= (180)0
⇒ (62)0 + x0 = (180)0
⇒ x0 = (180)0 – (62)0 = (118)0

2: In the adjoining figure, AOB is a straight line. Find the value of x.
Hence, find ∠AOC and ∠BOD.

3: In the adjoining figure, AOB is a straight line. Find the value of x.
Hence, find ∠AOC,∠COD and ∠BOD.

4: In the adjoining figure, x : y : z = 5 : 4 : 6. If XOY is a straight line,
find the values of x, y and z.

5: In the adjoining figure, what value of x will make AOB, a straight line?

6: Two lines AB and CD intersect at O. If ∠AOC= (50)0 , find ∠AOD,∠BOD and ∠BOC.

7: In the adjoining figure, three coplanar lines AB, CD and EF intersect at a point O,
forming angles as shown. Find the values of x, y, z and t.

8: In In the adjoining figure, three coplanar lines AB, CD and EF intersect at a point O.
Find the value of x. Hence, find ∠AOD,∠COE and ∠AOE.

9: two adjacent angles on a straight line are in the ratio 5 : 4.
Find the measure of each one of these angles.

10: If two straight lines intersect each other in such a way that one of the angles formed measures (90)0, show that each of the remaining angles (90)0.

11: Two lines AB and CD intersect at a point O such that
∠BOC+∠AOD= (280)0 , as shown in the figure. Find all the four angles.

12: Two lines AB and CD intersect each other at a point O such that ∠AOC∶∠AOD=5:7.
Find all the angles.

13: In the given figure, three lines AB, CD and EF intersect at a point O such that
∠AOE= (35)0 and ∠BOD= (40)0 .
Find the measure of ∠AOC,∠BOF,∠COF and ∠DOE.

14: In the given figure, two lines AB and CD intersect at a point O such that
∠BOC= (125)0 . Find the value of x, y and z.

15: If two straight lines intersect each other then prove that the ray opposite
to the bisector of one of the angles so formed bisects the vertically opposite angle.

16: Prove that the bisectors of two adjacent supplementary angles include a right angle.

### RS Aggarwal Solutions Class 9 Maths Chapter 7 Lines and Angles Ex 7.3

1: In the given figure, l ∥ m and a transversal t cuts them. If  ∠1 = 1200, find the measure of each of the remaining marked angle.

2: In the given figure, l ∥ m and a transversal t cuts them. If  ∠7 = 800, find the measure of each the remaining marked angles.

3: in the given figure, l ∥ m and a transversal t cuts them. If ∠1 : ∠2 = 2:3, find the measure of each of the marked angle.

4: For what value of x will the lines l and m be parallel to each other?

5: for what value of x will the lines l and m be parallel to each other?

6: In the given figure, AB ∥ CD and BC∥ ED. Find the value of x.

7: In the given figure, AB ∥ CD∥ EF. Find the value of x.

8: In the given figure, AB ∥ CD. Find the value of x, y and z.

9: In each of the figures given below, AB∥ CD. Find the value of x in each case.

10: In the given figure, AB ∥ CD. Find the value of x.

11: 8: In the given figure, AB ∥ PQ. Find the value of x, and y.

12: In the given figure, AB ∥ CD. Find the value of x.

13: In the given figure, AB ∥ CD. Find the value of x.

14: In the given figure, AB ∥ CD. Find the value of x, y and z.

15:  In the given figure, AB ∥ CD.  Prove that ∠BAE – ∠ECD = ∠AEC

16: In the given figure, AB ∥ CD. Prove that p+q – r = 180

17: In the given figure AB∥ CD and EF∥ GH. Find the value of x, y and z.

18: In the given figure, AB∥ CD and a transversal t cuts them at E and F respectively. If EG and FG are the bisectors of  ∠BEF and ∠EFD respectively, prove that ∠EGF =900.

19: In the given figure, AB ∥ CD and a transversal t cuts them at E and F respectively. If FP and EQ are the bisectors of ∠AEF and ∠EFD respectively, prove that EP ∥ FQ.

20: In the given figure, BA∥ ED and BC ∥ EF. Show that  ∠ABC =∠DEF.

21: In the given figure, BA ∥ ED and BC ∥ EF. Show that ∠ABC+∠DEF = 1800.

22: In the given figure, m and n are two plane mirrors perpendiculars to each other. Show that the incident ray CA is parallel to the reflected ray BD.

23: Inn the figure given below, state which lines are parallel and why?

24: Two lines are respectively perpendicular to two parallel lines. Show that they are parallel to each other.

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