AP State Syllabus AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions and Answers.

AP State Syllabus 9th Class Maths Solutions 4th Lesson Lines and Angles InText Questions

Question
Observe your surroundings carefully and write any three situations of your daily life where you can observe lines and angles. [Page No. 71]
Solution:
The edges of a blackboard; the edges of a ruler/scale and the edges of a table gives the idea of lines and their corners give the idea of angles.

Question
Draw the pictures in your notebook and collect some pictures. [Page No. 71]
Solution:
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 1

Think, Discuss and Write

What is the difference between inter-secting lines and concurrent lines ? [Page No. 74]
Solution:
If the number of lines meeting at a point are only two then they are said to be intersecting lines whereas if the lines are three or more than three meeting at a point then they are said to be concurrent lines.
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 2

Do These

Question 1.
Write the complementary, supplementary and conjugate angles for the following angles, a) 45° b) 75° c) 215° d) 30° e) 60° f) 90° g) 180° [Page No. 76]
Solution:
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 3

Question 2.
Which pairs of the following angles become complementary or supplementary. [Page No. 76]
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 4
Solution:
The angles formed by the figures (i) and (ii) are complementary.
The angles formed by the figures (ii) and (iii) are supplementary.

AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions

Try This

Question 1.
Find the pairs of adjacent and non- adjacent angles in the given figures. [Page No. 77]
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 5
Solution:
In figure (i) ∠1 and ∠2 are pair of adjacent angles.
In figure (ii), no adjacent angles.
In figure (iii) (∠1, ∠2), (∠2, ∠3) are pairs of adjacent angles.
In figure (iv) ∠1 and Z2 are adjacent angles.

ii) List the adjacent angles in the given figure. [Page No. 77]
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 6
Solution:
In the given figure
(∠1, ∠2), (∠3, ∠4), (∠4,∠5) and (∠3, ∠5) are the pairs of adjacent angles.

AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions

Think Discuss and Write

Question
Linear pair of angles are always supplementary. But supplementary angles need not form a linear pair. Why ? [Page No. 77]
Solution:
A pair of supplementary angles need not necessarily a linear pair because they may exists in separate figures.

Activity

Measure the angles in the following figure and complete the table.
[Page No. 78]
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 7
Solution:
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 8

AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions

Measure the four angles 1,2,3,4 in each of the above figure and complete the table:
[Page No. 79]
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 9
Solution:
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 10

AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions

Do This

Question 1.
Classify the given angles as pairs of complementary, linear pair, vertically opposite and adjacent angles. [Page No. 80]
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 11
Solution:
The pairs of angles a and b in the fig.(i) are linear pair of angles.
The pairs of angles a and b in the fig.(ii) are adjacent angles.
The pairs of angles a and b in the fig.(iii) are complementary angles*
The pairs of angles a and b in the fig.(iv) are vertically opposite angles.

Question 2.
Find the measure of angle ‘a’ in each figure. Give reasons in each case. [Page No. 81]
i)
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 12
a = 180° – 50° = 130°
(linear pair of angles)

AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions

ii)
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 13
a = 43°
( ∵ vertically opposite angles)

iii)
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 14
a = 360° – (209° + 96°)
= 360° – 305° = 55°
(∵ complete angle = 360°)

iv)
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 15
a = 90° – 63° = 27°
(pair of complementary angles )

AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions

Do These

Question 1.
Find the measure of each angle indi-cated in each figure where / and m are parallel lines intersected by a transversal n. [Page No. 87]
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 16
Solution:
x = 110° (alternate exterior angles)

AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions

AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 17
Solution:
y = 84° (alternate interior angles)

AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 18
Solution:
z = 180° – 100° = 80° .
(interior angles on the same side of transversal)

AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 19
Solution:
s° = 53° (pair of corresponding angles)

AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions

Question 2.
Solve for x and give reasons. [Page No. 88]
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 20
11x + 2 = 75°
11x = 75 – 2 = 73
∴ x = \(\frac{73}{11}\)
(∴ pair of corresponding angles are equal).

AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 21
Solution:
8x – 4 = 60°
8x = 60 + 4 = 64
∴ x = \(\frac{64}{8}\) = 8
(∴ alternate interior angles are equal)

AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 22
Solution:
(14x- 1)°.= (12x + 17)°
14x – 12x = 17 + 1
2x = 18
x = \(\frac{18}{2}\) = 9
(∴ alternate exterior angles are equal)

AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 23
Solution:
13x- 5 = 17x + 5
13x- 17x = 5 + 5
– 4x = 10
x = \(\frac{10}{-4}=\frac{-5}{2}\)
(∴ Pair of, corresponding angles are equal).

AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions

Activity

Question 1.
Take a scale and a ‘set sqaure’. Arrange the set sqare on the scale as shown in figure. Along the slant edge of set sqare draw a line with the pencil. Now slide your set square along its horizontal edge and again draw a line. We observe that the lines are parallel. Why are they parallel ? Think and discuss with your friends. [Page No. 88]
Solution:
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 24

A. Student Activity (For Reference .)
All slant lines are parallel making an angle of 60° with the horizontal line. In this figure horizontal line is transversal to the slant line and corresponding angles are equal.

Do This

Question
Draw a line \(\overline{\mathbf{A D}}\) and mark points B and C on it. At B and C, construct ∠ABQ and ∠BCS equal to each other as shown. Produce QB and SC on the other side of AD to form two lines PQ and RS.

Draw common perpendiculars EF and GH for the two lines PQ and RS. Measure the lengths of EF and GH. What do you observe ? What can you conclude from that ? Recall that if the perpendicular distance between two lines is the same, then they are parallel lines. [Page No. 89]
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 25
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 26
Solution:
As ∠ABQ =∠BCS and they lie on the same line AD we can say that BQ // CS. Now EF and GH are the perpendicular distances between two parallel lines PQ and R, we say EF = GH.

AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions

Try This

Question i)
Find the measure of the question marked angle in the given figure. [Page No. 90]
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 27
Solution:
? = 70°
[ ∵ from the figure, these two angles are exterior angles on the same side of the transversal]

ii) Find the angles which are equal to ∠P.
Solution:
∠P = ∠Q = ∠R = 110°
(corresponding angles)

Activity

Question
Draw and cut out a large triangle as shown in the figure.
Number the angles and tear them off.
Place the three angles adjacent to each other to form one angle as shown below. [Page No. 97]
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 28
1. Identify angle formed by the three adjacent angles ? What is its mea-sure ?
2. Write about the sum of the measures of the angles of a triangle. Now let us prove this statement
using the axioms; and theorems related to parallel lines.
Solution:
Student Activity.

AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions

Think, Discuss and Write

Question
If the sides of a triangle are produced in order, what will be the sum of exterion angles formed ? [Page No. 99]
Solution:
Let ΔABC and the sides of the triangle is formed by exterior angles.
AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions 29
∠3 = ∠B + ∠C
∠1 + ∠2 + Z∠3 = 2[∠A + ∠B + ∠C]
= 2 x 180° = 360°
∴ Sum of the exterior angles are 360°.

AP Board 9th Class Maths Solutions