AP Board Class 9 Maths Chapter 4 Lines and Angles Ex 4.2 Textbook Solutions PDF: Download Andhra Pradesh Board STD 9th Maths Chapter 4 Lines and Angles Ex 4.2 Book Answers ~ HSSlive: Plus One & Plus Two Notes & Solutions for Kerala State Board

AP Board Class 9 Maths Chapter 4 Lines and Angles Ex 4.2 Textbook Solutions PDF: Download Andhra Pradesh Board STD 9th Maths Chapter 4 Lines and Angles Ex 4.2 Book Answers

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Andhra Pradesh Board Class 9th Maths Chapter 4 Lines and Angles Ex 4.2 Textbooks Solutions PDF

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Andhra Pradesh State Board Class 9th Maths Chapter 4 Lines and Angles Ex 4.2 Books Solutions

Board	AP Board
Materials	Textbook Solutions/Guide
Format	DOC/PDF
Class	9th
Subject	Maths
Chapters	Maths Chapter 4 Lines and Angles Ex 4.2
Provider	Hsslive

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AP State Syllabus 9th Class Maths Solutions 4th Lesson Lines and Angles Exercise 4.2

Question 1.
In the given figure three lines AB⎯⎯⎯⎯⎯⎯⎯⎯ , CD⎯⎯⎯⎯⎯⎯⎯⎯ and EF⎯⎯⎯⎯⎯⎯⎯ intersecting at ‘O’. Find the values of x, y and z, it is being given that x : y : z = 2 : 3 : 5

Solution:
From the figure
2x + 2y + 2z = 360°
⇒ x + y + z = 180°
x : y : z = 2 : 3 : 5
Sum of the terms of the ratio
= 2 + 3 + 5 = 10

Question 2.
Find the value of x in the following figures.
i)

Solution:
From the figure
3x + 18= 180° – 93° (∵ linear pair )
3x + 18 = 87
3x = 87- 18 = 69
∴ x = 693 = 23

ii)

Solution:
From the figure
(x – 24)° + 29° + 296° = 360“
(∵ complete angle)
x + 301° = 360°
∴ x = 360° – 301° = 59°

iii)

Solution:
From the figure
2 + 3x = 62
(∵ vertically opposite angles)
3x = 62 – 2
∴ 3x = 60° ⇒ x = 603
∴ x = 20°

iv)

Solution:
From the figure
40 + (6x + 2) = 90°
(∵ complementary angles)
6x = 90° – 42°
6x = 48
x = 486 = 8°

Question 3.
In the given figure lines AB⎯⎯⎯⎯⎯⎯⎯⎯ and CD⎯⎯⎯⎯⎯⎯⎯⎯ intersect at ’O’. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.

Solution:
Given that ∠AOC +∠BOE = 70°
∠BOD = 40°
∠AOC = 40°
(∵ ∠AOC, ∠BOD are vertically opposite angles)
∴ 40° + ∠BOE = 70°
⇒ ∠BOE = 70° – 40° = 30°
Also ∠AOC + ∠COE +∠BOE = 180°
( ∵ AB is a line)
⇒ 40° + ∠COE + 30° = 180°
⇒ ∠COE = 180° -70° = 110°
∴ Reflex ∠COE = 110°

Question 4.
In the given figure lines XY⎯⎯⎯⎯⎯⎯⎯⎯⎯ and MN⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ . intersect at O. If ∠POY = 90° and a : b = 2:3, find c.

Solution:
Given that XY and MN are lines.
∠POY = 90°
a : b = 2 : 3
From the figure a + b = 90°
Sum of the terms of the ratio a : b
= 2 + 3 = 5
∴ b = 35 x 90° = 54°
From the figure b + c = 180°
(∵ linear pair of angles)
54° + c = 180°
c = 180°-54° = 126°

Question 5.
In the given figure ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT.

Solution:
Given that ∠PQR = ∠PRQ
From the figure
∠PQR + ∠PQS = 180° ………….. (1)
∠PRQ + ∠PRT = 180° …………..(2)
From (1) and (2)
∠PQR + ∠PQS = ∠PRQ + ∠PRT
But ∠PQR = ∠PRQ
So ∠PQS = ∠PRT
Hence proved.

Question 6.
In the given figure, if x + y = w + z, then prove that AOB is a line.

Solution:
Given that x + y = w + z = k say
From the figure
x + y + z + w = 360°
(∵ Angle around a point)
Also x + y = z + w
∴ x + y = z + w = 360∘2
∴ x + y = z + w = 180°

k + k = 360°
2k = 360°
k = 360∘2

(i.e.) (x,y) and (z, w) are pairs of adjacent angles whose sum is 180°.
In other words (x, y) and (z, w) are linear pair of angles ⇒ AOB is a line.

Question 7.
In the given figure PQ⎯⎯⎯⎯⎯⎯⎯⎯ is a line. Ray OR⎯⎯⎯⎯⎯⎯⎯⎯ is perpendicular to line PQ⎯⎯⎯⎯⎯⎯⎯⎯.OS⎯⎯⎯⎯⎯⎯⎯⎯ os is another ray lying between rays OP⎯⎯⎯⎯⎯⎯⎯⎯ and OR⎯⎯⎯⎯⎯⎯⎯⎯ Prove that

Solution:
Given : OR ⊥ PQ ⇒ ∠ROQ = 90°
To prove: ∠ROS = 12 (∠QOS – ∠POS)
Solution:
Proof: From the figure
∠ROS = ∠QOS – ∠QOR ……………(1)
∠ROS = ∠ROP – ∠POS ……………..(2)
Adding (1) and (2)
∠ROS + ∠ROS = ∠QOS – ∠QOR +∠ROP – ∠POS [ ∵ ∠QOR = ∠ROP = 90° given]
⇒ 2∠ROS = ∠QOS – ∠POS
⇒ ∠ROS = 12 [∠QOS – ∠POS]
Hence proved.

Question 8.
It is given that ∠XYZ = 64° and XY is produced to point P. A ray YQ⎯⎯⎯⎯⎯⎯⎯⎯⎯ bisects ∠ZYP. Dräw a figure from the given Information. Find ∠XYQ and reflex ∠QYP.
Solution:

∠XYQ = 32°
∠QYP = 32°

AP Board Textbook Solutions PDF for Class 9th Maths

Andhra Pradesh Board Class 9th Maths Chapter 4 Lines and Angles Ex 4.2 Textbooks for Exam Preparations

Andhra Pradesh Board Class 9th Maths Chapter 4 Lines and Angles Ex 4.2 Textbook Solutions can be of great help in your Andhra Pradesh Board Class 9th Maths Chapter 4 Lines and Angles Ex 4.2 exam preparation. The AP Board STD 9th Maths Chapter 4 Lines and Angles Ex 4.2 Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 9th Maths Chapter 4 Lines and Angles Ex 4.2 Books State Board syllabus with maximum efficiency.

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