Ch.4 Angles and Pairs of angles

04.Angles and Pairs of Angles

TextBook Page No 25:

PRACTICE SET 15

Question 1:

Observe the figure and complete the table for ∠AWB.

 

Points in the interior
Points in the exterior
Points on the arms of the angles

 

ANSWER:

Points in the interior	R, C, N, X
Points in the exterior	T, U, Q, V, Y
Points on the arms of the angles	A, W, G, B

Page No 25:

Question 2:

Name the pairs of adjacent angles in the figures below.

ANSWER:

Two angles which have a common vertex, a common arm and separate interiors are said to be adjacent angles.
The pairs of adjacent angles are given below:
∠ANB and ∠BNC,
∠BNC and ∠ANC,
∠ANC and ∠ANB,
∠PQR and ∠PQT

Page No 25:

Question 3:

Are the following pairs adjacent angles? If not, state the reason.

(i) ∠PMQ and ∠RMQ        (ii) ∠RMQ and ∠SMR

(iii) ∠RMS and ∠RMT      (iv) ∠SMT and ∠RMS

ANSWER:

Two angles which have a common vertex, a common arm and separate interiors are said to be adjacent angles
(i)
In ∠PMQ and ∠RMQ, M is the common vertex and MQ is the common arm.
Therefore, ∠PMQ and ∠RMQ are adjacent angles.     
(ii) 
The angles ∠RMQ and ∠SMR have a common vertex M, but don't have common arm.
Therefore, ∠RMQ and ∠SMR are not adjacent angles.     
(iii)
The angles ∠RMS and ∠RMT have a common vertex M, but don't have common arm.
Therefore, ∠RMS and ∠RMT are not adjacent angles.   
(iv)
In ∠SMT and ∠RMS, M is the common vertex and SM is the common arm.
Therefore, ∠SMT and ∠RMS are adjacent angles.

Page No 26:

PRACTICE SET 16

Question 1:

The measures of some angles are given below. Write the measures of their complementaryangles.

(i) 40^°   (ii) 63^° (iii) 45^°(iv) 55^° (v) 20^° (vi) 90^°  (vii) x^°

ANSWER:

(i)
Let the measure of the complementary angle be a.
40 + a = 90
 ∴ a = 50°
Hence, the measure of the complement of an angle of measure 40° is 50°
(ii)
Let the measure of the complementary angle be a.
63 + a = 90
 ∴ a = 27°
Hence, the measure of the complement of an angle of measure 63° is 27°
(iii)
Let the measure of the complementary angle be a.
45 + a = 90
 ∴ a = 45°
Hence, the measure of the complement of an angle of measure 45° is 45°
(iv)
Let the measure of the complementary angle be a.
55 + a = 90
 ∴ a = 35°
Hence, the measure of the complement of an angle of measure 55° is 35°
(v)
Let the measure of the complementary angle be a.
20 + a = 90
 ∴ a = 70°
Hence, the measure of the complement of an angle of measure 20° is 70°
(vi)
Let the measure of the complementary angle be a.
90 + a = 90
 ∴ a = 0°
Hence, the measure of the complement of an angle of measure 00° is 0°
(vii)
Let the measure of the complementary angle be a.
x + a = 90
 ∴ a = (90 − x)°
Hence, the measure of the complement of an angle of measure x° is (90 − x)°

Page No 26:

Question 2:

(y − 20)^° and (y + 30)^° are the measures of complementary angles. Find the measure of each angle.

ANSWER:

Sum of two complementary angles is 90^°
∴ (y − 20)^° + (y + 30)^° = 90^°
⇒ y − 20 + y + 30 = 90
⇒ 2y + 10 = 90
⇒ 2y = 80
⇒ y = 40

substitute the value of Y

y - 20

= 40 - 20

= 20

------------

y + 30

40 + 30

= 70

Hence, the measure of the two angles are 20^° and 70^°.
 

Page No 27:

PRACTICE SET NO.17

Question 1:

Write the measures of the supplements of the angles given below.

(i) 15^°  (ii) 85^° (iii) 120^° (iv) 37^° (v) 108^°  (vi) 0^° (vii) a^°

ANSWER:

(i)
Let the measure of the supplementary angle be a.
15 + a = 180
 ∴ a = 165°
Hence, the measure of the supplement of an angle of measure 15° is 165°.
(ii)
Let the measure of the supplementary angle be a.
85 + a = 180
 ∴ a = 95°
Hence, the measure of the supplement of an angle of measure 85° is 95°.
(iii)
Let the measure of the supplementary angle be a.
120 + a = 180
 ∴ a = 60°
Hence, the measure of the supplement of an angle of measure 120° is 60°.
(iv)
Let the measure of the supplementary angle be a.
37 + a = 180
 ∴ a = 143°
Hence, the measure of the supplement of an angle of measure 37° is 143°.
(v)
Let the measure of the supplementary angle be a.
108 + a = 180
 ∴ a = 72°
Hence, the measure of the supplement of an angle of measure 108° is 72°.
​(vi)
Let the measure of the supplementary angle be a.
0 + a = 180
 ∴ a = 180°
Hence, the measure of the supplement of an angle of measure 0° is 180°.
(vii)
Let the measure of the supplementary angle be x.
a + x = 180
 ∴ x = (180 − a)°
Hence, the measure of the supplement of an angle of measure a° is (180 − a)°.

Page No 27:

Question 2:

The measures of some angles are given below. Use them to make pairs of  complementary and supplementary angles.

m∠B = 60^° m∠N = 30^° m∠Y = 90^°  m∠J = 150^°
m∠D = 75^° m∠E = 0^° m∠F = 15^° m∠G = 120^°

ANSWER:

If the sum of the measures of two angles is 90° they are known as complementary angles. 
Hence,the pairs of complementary angles are ∠B and ∠N, ∠D and ∠F, ∠Y and ∠E.
If the sum of the measures of two angles is 180° they are known as supplementary angles. 
Hence, the pairs of supplementary angles are ∠B and ∠G, ∠N and ∠J.

Page No 27:

Question 3:

In ∆XYZ, m∠Y = 90^°. What kind of a pair do ∠X and ∠Z make?

ANSWER:

In ∆XYZ,
∠X + ∠Y + ∠Z = 180^°    (Angle Sum property of triangle
⇒ ∠X + 90^° + ∠Z = 180^°
⇒ ∠X + ∠Z = 90^°
Since, the sum of the measure of the two angles is 90^°.
Hence, ∠X and ∠Z are complementary angles.

Page No 27:

Question 4:

The difference between the measures of the two angles of a complementary pair is  40^°. Find the measures of the two angles.

ANSWER:

Let the measure of the first angle a.
Then, the measure of the other angle a + 40°
Now, a + a + 40 = 90
⇒ 2a = 50
⇒ a = 25°
Hence, the measure of the two angles are 25° and 65°.

Page No 27:

Question 5:

□$\square$ PTNM is a rectangle. Write the names of the pairs of supplementary angles.

ANSWER:

If the sum of the measures of two angles is 180° they are known as supplementary angles. 
The measure of all the angles of a rectangle is 90°.
Hence, the pairs of supplementary angles are ∠P and ∠M, ∠T and ∠N, ∠P and ∠T, ∠M and ∠N, ∠P and ∠N, ∠M and ∠T.

Page No 27:

Question 6:

If m∠A = 70^°, what is the measure of the supplement of the complement of ∠A?

ANSWER:

Let the measure of the complementary angle be a.
70 + a = 90
 ∴ a = 20°
Let the measure of the supplementary angle of 20° be x.
20 + x = 180
 ∴ x = 160°
Hence, the measure of the supplement of the complement of ∠A is 160°.
 

Page No 27:

Question 7:

If ∠A and ∠B are supplementary angles and m∠B = (x + 20)^°, then what would be m∠A?

ANSWER:

Let the measure of the supplementary angle of ∠B be a.
(x + 20)^° + a = 180
 ∴ a = (160 − x)°
Hence, the measure of ∠A is (160 − x​)°.

Page No 28:

Practice SetNo.18

Question 1:

Name the pairs of opposite rays in the figure alongside.

ANSWER:

Two rays which have a common origin and form a straight line are said to be opposite rays. 
Hence, the pairs of opposite rays are ray PL & ray  PM and ray PN & ray PT.

Page No 28:

Question 2:

Are the ray PM and PT opposite rays?  Give reasons for your answer.

ANSWER:

Ray PM and PT are not opposite rays because they do not form a straight line.

Page No 29:

PRACTICE SET NO.19

Question 1:

Draw the pairs of angles as described below.If that is not possible, say why.

(i)  Complementary angles that are not adjacent.

(ii)   Angles in a linear pair which are not supplementary.

(iii)   Complementary angles that do not form a linear pair.

(iv)  Adjacent angles which are not in a linear pair.

(v)   Angles which are neither complementary nor adjacent.

(vi)   Angles in a linear pair which are complementary.

ANSWER:

(i)  


(ii)   

If the sum of the measures of two angles is 180° they are known as supplementary angles.
The sum of the measures of the angles in a linear pair is 180°.
Therefore, angles in a linear pair are always supplementary.

(iii)   

(iv)  

(v)   

(vi)   
If the sum of the measures of two angles is 180° they are known as supplementary angles.
The sum of the measures of the angles in a linear pair is 180°.
Therefore, angles in a linear pair are always supplementary.

Page No 30:

PRACTICE SET NO.20

Question 1:

Lines AC and BD intersect at point P. m∠APD = 47^° .Find the measures of ∠APB, ∠BPC, ∠CPD.

ANSWER:

In the given figure, 
∠DPA + ∠APB = 180^∘         (Linear Pair angles)
⇒ 47^∘ + ∠APB = 180^∘
⇒ ∠APB = 133^∘
Now, 
∠APD = ∠BPC = 47^∘          (Vertically opposite angles)
∠APB = ∠DPC = 133^∘          (Vertically opposite angles)
Hence, the measures of ∠APB, ∠BPC, ∠CPD are 133^∘, 47^∘ and 133^∘ respectively.

Page No 30:

Question 2:

Lines PQ and RS intersect at point M. m∠PMR = x^° What are the measures of ∠PMS, ∠SMQ and ∠QMR?


 

ANSWER:

In the given figure, 
∠RMP + ∠PMS = 180^∘         (Linear Pair angles)
⇒ x^∘ + ∠PMS = 180^∘
⇒ ∠PMS = (180 − x)^∘
Now, 
∠PMR = ∠SMQ = x^∘                       (Vertically opposite angles)
∠PMS = ∠RMQ = (180 − x)^∘          (Vertically opposite angles)
Hence, the measures of ∠PMS, ∠SMQ and ∠QMR are (180 − x)^∘, x^∘ and (180 − x)^∘ respectively.

Page No 33:

PRACTICE SET NO.21

Question 1:

∠ACD is an exterior angle of Δ$∆$ABC.The measures of ∠A and ∠B are equal. If m∠ACD = 140^°, find the measures of the angles ∠A and ∠B.

ANSWER:

∠A + ∠B = ∠ACD   (Exterior angle property)
⇒ 2∠A = 140^∘         (∵∠A = ∠B)        
⇒ ∠A = 70^∘
Hence, the measures of ∠A and ∠B are 70^∘ and 70^∘ respectively.

Page No 33:

Question 2:

Using the measures of the angles given in the figure alongside, find the measures of the remaining three angles.

ANSWER:

In the given figure, 
∠BOC = ∠FOE = 4y           (Vertically opposite angles)
∠EOD = ∠AOB = 8y           (Vertically opposite angles)
∠AOF = ∠COD = 6y           (Vertically opposite angles)
Now, ∠AOB + ∠BOC + ∠COD = 180^∘         (Linear Pair angles)
⇒ 8y + 4y + 6y = 180^∘
⇒ 18y = 180^∘
⇒ y = 10^∘
Therefore, 
∠BOC = 4y
= 40^∘
∠EOD = 8y
= 80^∘
​∠AOF = 6y
= 60^∘
Hence, the measures of ∠BOC, ∠EOD, ∠AOF are 40^∘, 80^∘ and 80^∘ respectively.

Page No 33:

Question 3:

In the isosceles triangle ABC, ∠A and ∠B are equal. ∠ACD is an exterior angle of ∆ABC. The measures of ∠ACB and ∠ACD are
(3x−$-$17)^° and (8x + 10)^° respectively. Find the measures of ∠ACB and ∠ACD. Also find the measures of ∠A and ∠B.

ANSWER:

Given:
∠ACB = (3x −$-$ 17)^∘
∠ACD = (8x + 10)^∘
Now, ∠ACB + ∠ACD = 180^∘         (Linear Pair angles)
⇒ 3x − 17 + 8x + 10 = 180
⇒ 11x = 187
⇒ x = 17
Therefore,
∠ACB = (3x −$17)^\circ$= (51 −17)$^<br>$= 34^∘
​∠ACD = (8x + 10)^∘
= (136 + 10)^∘
= 146^∘
Now, ∠A + ∠B = ∠ACD   (Exterior angle property)
⇒ 2∠A = 146^∘         (∵∠A = ∠B)        
⇒ ∠A = 73^∘
Hence, the measures of ∠ACB, ∠ACD, ∠A and ∠B are 146^∘, 34^∘, 73^∘ and 73^∘ respectively.

 

Std.7 Problem Set No.14 Q.No.9

Std.VII Q.9 Problem set No.14

IDEA Competition- Innovators of Tomorrow

THE IDEA

STUDENT INNOVATION COMPETITION

The IDEA Competition is intended to spark the entrepreneurial spirit and accelerate the development of creative innovation.

The objective of the competition is to target original ideas/innovations rooted in science and societal applications to foster a culture of creativity and innovative thinking among school children.

Few examples:

Submit your ORIGINAL IDEA in the above format before 20th August 2021.

05 Best Ideas will be sent to the next level.

(For INSPIRE AWARDS)

Ch.9 Motion and Types of Motion

Question 1:

Identify the types of motion.
(a) Movement of the earth around the sun : .......... .
(b) Movement of a ceiling fan : ..........
(c) A meteor falling from the sky : .......... .
(d) A rocket launched from the ground : ..........
(e) A fish swimming in water : ..........
(f) The plucked string of a sitar : .......

ANSWER:

(a) Movement of the earth around the sun : Circular and periodic motion.
(b) Movement of a ceiling fan : Circular motion.
(c) A meteor falling from the sky : Non-uniform linear motion.
(d) A rocket launched from the ground : Non-uniform linear motion.
(e) A fish swimming in water : Random motion.
(f) The plucked string of a sitar : Oscillatory motion

Page No 69:

Question 2:

Fill in the blanks.
(a) If a ball is released from the terrace of a building, it comes down in ........... motion. On the other hand, it reaches the ground in ........... motion if it is thrown with force away from the terrace in a direction parallel to the terrace.
(b) The motion of an aeroplane on the runway before take-off is.......... .
(c) The kite looking for its prey flies with .......... motion in the sky.
(d) Children sitting in a rotating giant wheel have ........... motion, while those sitting in a merry-go-round have a ........... motion.
(Linear, non-linear, circular, uniform linear, non-uniform linear, uniform circular, non-uniform circular, random)

ANSWER:

(a) If a ball is released from the terrace of a building, it comes down in non-uniform linear motion. On the other hand, it reaches the ground in non-linear motion if it is thrown with force away from the terrace in a direction parallel to the terrace.
(b) The motion of an aeroplane on the runway before take-off is non-uniform linear motion .
(c) The kite looking for its prey flies with random motion in the sky.
(d) Children sitting in a rotating giant wheel have non-uniform circular motion, while those sitting in a merry-go-round have a uniform circular motion.

Page No 69:

Question 3:

How are we different?
(a) Oscillatory motion and linear motion.
(b) Linear motion and random motion.
(c) Random motion and oscillatory motion.

ANSWER:

(a) 

Oscillatory motion	Linear motion
The type of motion in which the object moves back and forth repeatedly is known as oscillatory motion.	The type of motion in which the object moves from one point to another in a straight line is called linear motion.
For example: Movement of the pendulum of a clock	For example: Vehicles moving on a straight road

(b)

Linear motion	Random motion
The type of motion in which the object moves from one point to another in a straight line is called linear motion.	The type of motion in which the direction of motion and the speed of an object changes continuously is called random motion.
For example: Vehicles moving on a straight road	For example: Children playing in a garden

(c) 

Random motion	Oscillatory motion
The type of motion in which the direction of motion and the speed of an object changes continuously is called random motion.	The type of motion in which the object moves to and fro repeatedly about a mean or a fixed position is known as oscillatory motion.
For example: Children playing in a garden	For example: Movement of the pendulum of a clock

Page No 69:

Question 4:

Explain in your own words, giving one example each.
(a) Linear motion
(b) Oscillatory motion
(c) Circular motion
(d) Random motion
(e) Periodic motion

ANSWER:

(a) Linear motion: An object is said to have linear motion if it moves from one point to another in a straight line. For example: The motion of a moving car on a straight road.

(b) Oscillatory motion: The type of motion in which the object moves to and fro repeatedly about a mean or a fixed position is known as oscillatory motion. For example: The movement of pendulum of a clock.

(c) Circular motion: An object is said to possess circular motion if it moves from one point to another in such a way that its distance from a fixed point always remains constant. For example: The movement of the blades of a fan.

(d) Random motion: The type of motion in which the direction of motion and the speed of an object changes continuously is called random motion. For example: Children playing in a garden.

(e) Periodic motion: An object is said to possess periodic motion if it moves in such a way that it repeats its motion after a certain interval of time. For example: The motion of a swing.

Page No 69:

Question 5:

Answer the following questions in your own words.
(a) Which types of motion are seen in birds flying in the sky ?
(b) Write in detail about your experience of various types of motion while riding a bicycle on a road.

ANSWER:

(a) Birds flying in the sky have random motion as their direction of motion and speed continuously changes.

(b) While riding a bicycle on a road, following types of motion can be seen:

• The wheels of the bicycle are in uniform or non-uniform circular.
• The legs of the person riding the bicycle are in uniform or non-uniform circular motion.
• The bicycle is in uniform or non-uniform linear motion. It can also be in non-uniform motion.

Page No 69:

Question 6:

Complete the puzzle using words for types of motion :
(1) a spring is stretched and one end is released
(2) a minute hand
(3) a see saw
(4-5) children in a march past
(6) a stone rolling down a hillside.

ANSWER:

courtesy:

https://www.meritnation.com/maharashtra-class-6/science/general-science-solutions/motion-and-types-of-motion/textbook-solutions/87_2_3388_24483_69_136857

Paper Pattern & Portion Class:V

 UNIT TEST EXAMINATION (2021-2022)                                                                              STD.V                                                    SUBJECT: EVS I  MARKS-10  TIME: 01 HR

 

Q.1. A) Choose the correct alternative and write it along with it allotted alphabet.  01 Mark                        

B) Answer the following  01 Mark                  

Q.2 A) Give Reasons: (Any 01)    01 Mark       

 B) Answer the following (Any 02) 04 Marks  

Q.3 Answer the following:(Any 01) 03 Marks

Portion:

Ch.1- Our Earth and Our Solar System

Ch.2- Motions of the Earth

Ch.3- The Earth and Its Living World

Ch.2 Motions of the Earth

Chp 2. MOTIONS OF THE EARTH

 

1. What’s the solution ?

Amit wants to take his granny to Australia which is in the southern hemisphere. But she cannot bear very cold weather. When should they make this trip ?

Ans. (a) Amit’s granny cannot bear cold weather. Hence, she should visit Australia during summer. (b) Australia is situated in the southern hemisphere. It experiences summer season during the period of 23rd September to 22nd March. (c) Considering this, they should make the trip to Australia anytime between October to mid-March.

 2. Use your brain power!

(i) How many rotations does the earth complete during one revolution around the sun?

 Ans: The earth completes one rotation in 1 day. It takes 365 days and 6 hours i.e., 1/4 day to complete one revolution. This means, during one revolution around the sun, the earth performs 365 and 1/4 rotations.

 (ii) It is sunrise at Itanagar in Arunachal Pradesh. Write the names of the following cities in the order in which the sun will rise there. Mumbai (Maharashtra), Kolkata (West Bengal), Bhopal (Madhya Pradesh), Nagpur (Maharashtra).

Ans: The earth rotates from west to east. The sunrise is observed earlier in the eastern states and gradually it is seen by western states of India. The order in which the sun will rise in the given cities is: Itanagar (Arunachal Pradesh), Kolkata (West Bengal), Nagpur (Maharashtra), Bhopal (Madhya Pradesh) and Mumbai (Maharashtra)

3.Fill in the blanks

(You must write the answers for this question on your own)

4. What is meant by each of the following terms?

 (i) Full moon (ii) New moon (iii) Lunar month (iv) Tithi

 Ans: (i) Full moon: When a complete and round moon is seen in the sky, it is called as full moon.

 (ii) New moon: When the moon is not at all visible in the sky from the earth, it is called as new moon.

 (iii) Lunar month: The duration of 28 to 30 days between a new moon to the next new moon is called a lunar month.

 (iv) Tithi: Every day of the lunar month is called as tithi.

5. Answer the following questions.

(i) What is the equator?
 Ans: (i) An imaginary circle around the surface of the earth, exactly in between the north and south poles is called the equator.

(ii) What are the two parts of the earth made by the equator ?

Ans: The two parts of the earth made by the equator are: (a) Northern hemisphere (b) Southern hemisphere

**********************************************************