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Complementary Angles, Suplementary Angles And Adjacent Angles

Class 8th Mathematics West Bengal Board Solution
Lets Do 6.1
  1. Let's find which pair of angles are complementary or supplementary among the following…
Lets Do 6.2
  1. Which of following figures having the sun I adjacent angles as two right angles? k sum…
  2. Let's draw a straight line AB and consider a point P on the line AB. Let's erect a ray…
Lets Work Out 6
  1. Let’s write whether two acute angles are complementary to each other. Let’s think and…
  2. Let’s write whether two acute angles are supplementary to each other. Let’s think and…
  3. Let’s write whether one acute angle and one obtuse angle which are complementary to…
  4. Let’s write whether two obtuse angles are supplementary to each other. Let’s think and…
  5. Let’s write whether two right angles are supplementary to each other. Let’s think and…
  6. Let’s write whether one acute angle and one obtuse angle are supplementary to each…
  7. Let’s write whether two adjacent angles are complementary to each other. Let’s think…
  8. Let’s write whether two adjacent are supplementary to each other. Let’s think and…
  9. Let’s draw adjacent angles whose measurements are given below.Let’s examine which pair…
  10. Let’s see the measurement of the angles given below and examine which pair of angles…
  11. Let’s see the measurement of the angles given below and examine which pair of angles…
  12. Lets define adjacent angles and write which pair of angles are adjacent from the…
  13. Let’s draw adjacent angles by using protractor whose measurements are given below.35°,…
  14. Sayantani drew a straight line AB. I drew a ray PQ from a point P on AB. As a result…
  15. Shakil draws two adjacent angles ∠ABC and ∠ABD whose sum of measurement is 180°; I also…
  16. Let’s find the value of x from the figure beside.
  17. Let’s find the value of ∠AOP ∠BOP if the measurement of AOP is more than ∠BOP by…
  18. Measurement of two adjacent angles is 35° and 145°. Let’s write how the external sides…
  19. Let’s write how are the line segment OA and OE situated in the figure beside.…
Lets Do 6.1
Question 1.

Let's find which pair of angles are complementary or supplementary among the following pairs of angles and then draw:

10°, 170°; 38°, 52°; 35°, 65°; 90°, 90°; 25°, 165°; 45°, 45°
Answer:

Let us understand what complementary and supplementary angles are.

Complementary angles: When the sum of the measures of two angles is 90°, such angles are called complementary angles. Each angle is called complement of the other.


Supplementary angles: When the sum of the measures of two angles is 180°, such angles are called supplementary angles. Each angle is called supplement of the other.


Take pair 10° and 170°.


Now, adding them


10° + 170° = 180°


Thus, by definition 10° and 170° are supplementary angles.



Take pair 38° and 52°.


Now, adding them


38° + 52° = 90°


Thus, by definition 38° and 52° are complementary angles.



Take pair 35° and 65°.


Now, adding them


35° + 65° = 100°


Thus, by definition 35° and 65° are neither complementary nor supplementary angles.



Take pair 90° and 90°.


Now, adding them


90° + 90° = 180°



Take pair 25° and 165°.


Now, adding them


25° + 165° = 190°


Thus, by definition 25° and 165° are neither complementary nor supplementary angles.



Take pair 45° and 45°.


Now, adding them


45° + 45° = 90°


Thus, by definition 45° and 45° are complementary angles.
Lets Do 6.2
Question 1.

Which of following figures having the sun I adjacent angles as two right angles?
Answer:

Question 2.

Let's draw a straight line AB and consider a point P on the line AB. Let's erect a ray from P on the straight line AB. As a result two adjacent angles are formed. Now we measure the adjacent angles and examine whether the sum of the measurement of those angles is 180° or not.
Answer:

First, draw a straight line, naming it A.


Now, consider a point P anywhere on AB.



Now, from that P point, draw a ray in any direction.



Or,



We see that two adjacent angles are formed.


In either case, we can measure the angles by a protractor.


Let us take this,



In this case,


60° + 120° = 180°


Similarly, in every case,


If a straight line is partitioned, then the sum of (any) adjacent angles will be 180° every time.
Lets Work Out 6
Question 1.

Let’s think and write:

Let’s write whether two acute angles are complementary to each other.
Answer:

Yes, two acute angles are complementary to each other in case if sum of both the acute angles is equal to 90°


Example - 60° + 30° = 90°
Question 2.

Let’s think and write:

Let’s write whether two acute angles are supplementary to each other.
Answer:

No, acute angles are angles that measure greater than 0° and less than 90°

Supplementary angles are positive angles that add up to 180°.


If you add two acute angles that are each as large as possible, their sum will be less than 180°, so they can’t be supplementary.


Example - 89° + 89° = 178°
Question 3.

Let’s think and write:

Let’s write whether one acute angle and one obtuse angle which are complementary to each other. Also examine whether two right angles are complementary to each other.
Answer:

No, one acute angle and one obtuse angle cannot be complementary to each other because obtuse angles themselves are greater than 90°.


No, two right angles are not complementary to each other.
Question 4.

Let’s think and write:

Let’s write whether two obtuse angles are supplementary to each other.
Answer:

No, obtuse angles are angles that measure greater than 90° and less than 180°

Supplementary angles are positive angles that add up to 180°.


If you add two obtuse angles that are each as small as possible, their sum will be more than 180°, so they can’t be supplementary.


Example - 91° + 91° = 182°
Question 5.

Let’s think and write:

Let’s write whether two right angles are supplementary to each other.
Answer:

Yes, two right angles are supplementary to each other as right angles measure 90°.


Example - 90° + 90° = 180°
Question 6.

Let’s think and write:

Let’s write whether one acute angle and one obtuse angle are supplementary to each other.
Answer:

Yes, one acute angle and one obtuse angle are supplementary to each other.


Example - 89° + 91° = 180°
Question 7.

Let’s think and write:

Let’s write whether two adjacent angles are complementary to each other.
Answer:

Yes, two adjacent angles can be complementary, if they add upto 90°.

Example – In a right-angle triangle two adjacent angles are complementary.
Question 8.

Let’s think and write:

Let’s write whether two adjacent are supplementary to each other.
Answer:

Yes, in case of a linear pair two adjacent angles are supplementary to each other.
Question 9.

Let’s draw adjacent angles whose measurements are given below.

Let’s examine which pair of angles are complementary or supplementary to each other:

45°, 45° ; 120°, 30° ; 70°, 110° ; 42°,48° 37°, 43° ; 85°, 95°
Answer:

a)


As 45° + 45° = 90°


Hence these angles are complementary.



They are complementary to each other.


b)



As 120° + 30° = 150°


Hence these angles are niether complemenatry nor supplementary angles.


C)


As 70° + 110° = 180°



They are supplementary.


d)



They are complementary.


e)



f)



They are supplementary
Question 10.

Let’s see the measurement of the angles given below and examine which pair of angles are complementary to each other:

31°, 47°, 64°, 29°, 43°, 59°, 17°, 26°
Answer:

a) 59° and 31°

b) 47° and 43°


c) 64° and 26°


Following pair of angles are complementary to each other.
Question 11.

Let’s see the measurement of the angles given below and examine which pair of angles are supplementary to each other:

47°, 58°, 69°, 75°, 133°, 105°, 122°, 125°
Answer:

a) 47° and 133°

b) 58° and 122°


c) 75° and 105°


Following pair of angles are supplementary to each other.
Question 12.

Lets define adjacent angles and write which pair of angles are adjacent from the following figures.
Answer:

Two angles are Adjacent when they have a common side and a common vertex (corner point) and don't overlap.


a)∠A and ∠B are adjacent to each other.


b)∠A and ∠B are adjacent to each other.



∠A and ∠B are adjacent to each other.


∠A and ∠B are not adjacent to each other.
Question 13.

Let’s draw adjacent angles by using protractor whose measurements are given below.

35°, 45° ; 18°, 42° ; 32°, 90° ; 73°, 63°
Answer:

(a)



(b)



(c)



(d)
Question 14.

Sayantani drew a straight line AB. I drew a ray PQ from a point P on AB. As a result two adjacent angles ∠PQB and ∠PQA are formed. Let’s write the measurement of angles ∠PQB and ∠PQA are formed. Let’s write the measurement of angles ∠PQB and ∠PQA and ∠PQB + ∠PQA by using protractor.
Answer:

∠PQB = 100°


∠PQA = 80°


∠PQB + ∠PQA = 180°
Question 15.

Shakil draws two adjacent angles ∠ABC and ∠ABD whose sum of measurement is 180°; I also drew ∠ABC and ∠ABD like Shakil and examined whether point B,D and C lie on a same straight line or not.
Answer:

YES, points B, D and C lies on a straight line.
Question 16.

Let’s find the value of x from the figure beside.
Answer:

∠AOD = 3x°

∠DOC = 80°


∠COB = x°


∠AOD + ∠DOC + ∠COB = 180° (linear pair)


3x + x + 80° = 180°


4x = 180° – 80°


4x = 80°


x = 20°
Question 17.

Let’s find the value of ∠AOP & ∠BOP if the measurement of AOP is more than ∠BOP by 140°.
Answer:

According to question,

∠AOP = ∠BOP + 140° (1)


But ∠AOP + ∠BOP = 180° (Linear pair)


Put value of ∠AOP from (1)


∠BOP + 140° + ∠BOP = 180°


2∠BOP = 180° - 140°


2∠BOP = 40°


∠BOP = 20°


Put in (1)


∠AOP = ∠BOP + 140°


∠AOP = 20° + 140°


∠AOP = 160°
Question 18.

Measurement of two adjacent angles is 35° and 145°. Let’s write how the external sides of those two angles are situated?
Answer:


External sides of these angles make a straight line.
Question 19.

Let’s write how are the line segment OA and OE situated in the figure beside.
Answer:

∠EOD = 24°

∠DOC = 81°


∠COB = 55°


∠BOA = 20°


∠EOD + ∠DOC + ∠COB + ∠BOA


24° + 81° + 55° + 20° = 180°


Since, sum of all the angles is 180° it means that EOA is a straight line.


Thus, line segments OA and OE forms a straight line.