NCERT Solutions For Class 9 Maths Chapter 4 Lines and Angles Ex 4.2
Here, Below you all know about NCERT Solutions for Class 9 Maths Chapter 4 Lines and Angles Ex 4.2 Question Answer. I know many of you confuse about finding this Chapter 4 Lines and Angles Ex 4.2 Of Class 9 NCERT Solutions. So, Read the full post below and get your solutions.
Textbook | NCERT |
Board | CBSE |
Category | NCERT Solutions |
Class | Class 9 |
Subject | Maths |
Chapter | Chapter 4 |
Exercise | Class 9 Chapter 4 Lines and Angles Exercise 4.2 |
Number of Questions Solved | 6 |

NCERT Solutions for Class 9 Maths Chapter 4 Lines and Angles Ex 4.2
NCERT TEXTBOOK EXERCISES
Question 1. In figure, find the values of x and y and then show that AB || CD.

Solution:
∵ x + 50° = 180° (Linear pair)
⇒ x = 130°
∴ y = 130° (Vertically opposite angle)
Here, ∠x = ∠COD = 130°
These are corresponding angles for lines AB and CD.
Hence, AB || CD
Question 2. In figure, if AB || CD, CD || EF and y: z = 3:7, find x.

Solution:
Given

⇒ Let y = 3k, z = 7k
x = ∠CHG (Corresponding angles)…(i)
∠CHG = z (Alternate angles)…(ii)
From Eqs. (i) and (ii), we get
x = z …….(iii)
Now, x+y = 180°
(Internal angles on the same side of the transversal)
⇒ z+y = 180° [From Eq. (iii)]
7k + 3k = 180°
⇒ 10k = 180°
⇒ k = 18
∴ y = 3 x 18° = 54°
and z = 7x 18°= 126°
∴ x = z
Now, x + y = 180°
(Internal angles on the same side of the transversal)
⇒ z + y = 180° [From Eq. (iii)]
7k + 3k = 180°
⇒ 10k = 180°
⇒ k = 18
∴ y = 3 x 18° = 54°
and z = 7x 18°= 126°
x = z
⇒ x = 126°
Question 3. In figure, if AB || CD, EF ⊥ CD and ∠GED = 126°, find ∠AGE, ∠GEF and ∠FGE.

Solution:
∵ ∠AGE = ∠GED (Alternate interior angles)
But ∠GED = 126°
⇒ ∠AGE = 126° ….(i)
∴ ∠GEF + ∠FED= 126°
⇒ ∠GEF + 90° =126° (∵ EF ⊥ CD)
⇒ ∠GEF = 36°
Also, ∠AGE + ∠FGE = 180° (Linear pair axiom)
⇒ 126° + ∠FGE =180°
⇒ ∠FGE = 54°
Question 4. In figure, if PQ || ST, ∠ PQR = 110° and ∠ RST = 130°, find ∠QRS.

Solution:
Drawing a tine parallel to ST through R.


Question 5. In figure, if AB || CD, ∠APQ = 50° and ∠PRD = 127°, find x and y.

Solution:
We have, AB || CD
⇒ ∠APQ = ∠PQR (Alternate interior angles)
⇒ 50° = x
⇒ x = 50°
Now, ∠PQR + ∠QPR = 127°
(Exterior angle is equal to sum of interior opposite angles of a triangle)
⇒ 50°+ ∠QPR = 127°
⇒ y = 77°.
Question 6. In figure, PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB || CD.

Solution:

NCERT Solutions for Class 9 Maths Chapter 4 Lines and Angles Exercise 4.2 PDF
For NCERT Solutions for Class 9 Maths Chapter 4 Lines and Angles Ex 4.2, you may click on the link below and get your NCERT Solutions for Class 9 Maths Chapter 4 Lines and Angles Exercise pdf file.
Finally, You all know about NCERT Solutions for Class 9 Maths Chapter 4 Lines and Angles Ex 4.2. If you have any questions, then comment below and share this post with others.