Complementary Angles Supplementary Angles And Adjacent Angles
It is seen that the sum of ∠A and ∠E is 90° or one right angle. What can be termed such two angles?
If the sum of measurement of 2 angles is 90°, then they are called complementary angles to each other. Here the complementary angle of ∠A is ∠E and vice-versa. I got ∠E is the complementary angle ∠A ∠B [∠C /∠D]
Which pair among ∠H, ∠I and ∠L form complementary angles?
∠H and ∠I are complementary, and ∠l and ∠L are complementary to each other.
Now I write the measurement of the supplementary angle of ∠G and draw it with a protractor.
The supplementary angle of ∠G is = 180° – 118° – 62°
Read and Learn More WBBSE Solutions For Class 8 Maths
Complementary Angles Exercise
Question 1. Let’s find which pair of angles are complementary or supplementary among the following pairs of angles and then draw.
Solution:
10°, 170°; 38°, 52°; 35°, 65°; x90°, 90°; 25°, 165°; 45°, 45°
10°, 170° supplementary
90°, 90° supplementary
45°, 45° complementary
38°, 52° complementary
∠ABC and ∠CBD are supplementary angles.
∠MNO and ∠MNP supplementary.
∠WXY and ∠YXZ are supplementary angles.
∠PQR and ∠RQS are supplementary angles.
New we think whether are 1,2 are 4 ∠A and ∠B are adjacent angles.
In figures 2 and 3 one side of ∠A and ∠B aren’t complementary but in figure one side ∠A and ∠B is (ordinary) but on one side of there are two angles.
In figure, 3 the origin of both angles isn’t same.
In figure 4 both angles are adjacent angles because origin of both is same and on both sides, there are ∠A and ∠B.
Here we measure both [a] and \b\ are complementary angles. If ∠A = 65°, ∠B = 115°; then ∠A + ∠B = 180° degrees.
Now we see both adjacent angles ∠A and ∠B. are ∠A = 65 degrees. ∠B = 115 degrees and ∠A + ∠B = 180 degrees. My brother kept a pen in the pen-stand as is shown in the picture. We see that two adjacent angles adjacent ∠A and ∠B are formed. Measuring we get ∠A + ∠B = 180 degrees.
It is seen by measuring adjacent angles that ∠PQY= 45°, ∠PQX = 135° and ∠PQY + ∠PQX = 180° and ∠MND = 130°, ∠MNC = 50° and ∠MND + ∠MNC= 180°
It one ray is inclined on a straight line then two adjacent angles are formed. The sum of the measurement of them is equal to two right angles right angle or M 180 degrees.
Complementary Angles Exercise
Question 1. Let’s write the sum of measurements of which adjacent angles are two right angles in the figures below.
Solution:
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.
Solution:
On the line AB from the point P we draw a straight line, so are formed two adjacent angles ∠QPA and ∠QPB.
∠QPA = 60°, ∠QPB – 120°
The sum of the angles is = 60° + 120° = 180° or two right angles.
Now we will play a game with the help of three colourful sticks. We will form two angles whose sum total is 180° or 2 right angles joining one end of these colourful sticks. I formed
By stick ∠A and ∠B are termed.
∠A = 113°and ∠B = 67° ∠A + ∠B = 180 degree
The common side of two adjacent angles ∠A & ∠B is Green coloured stick. It is seen by drawing on the exercise book that two uncommon sides of two adjacent angles ∠A and ∠B, i.e., the red and the blue sticks lie on a straight line.
Zakir formed
Formed by sticks where ∠A = 70°, ∠B = 110°.
Here the common side of ∠A and ∠B is the green coloured stick.
It is seen by drawing on an exercise book that two uncommon sides of two adjacent angles ∠A ∠B, i.e., the red and the blue sticks lie on a straight line.
Julefa drew some angles in her exercise book and measured them with a protractor. She marked the angles.
Siraj will take two such angles from the angles drawn by Julefa, the sum of which is 180°or two right angles. Then he will see that the two exterior arms are in the same straight line.
At first, I took ∠ABC = 80°. New I took the supplementary 100 degrees or angle of ∠XYZ. Now I placed side AB of ∠ABC or the side XY of ∠XYZ.
It is seen that segments YZ and BE lie on the same straight line BC. Similarly, I placed the supplementary angle of 155 degrees of 25° as the figure beside.
It is seen that two line segments KL and EF lie on the same straight line.
∠PQR. Let’s draw adjacent angles with the angles whose measurements are given below and examine whether the external sides of those adjacent angles lie on a same straight line or not.
∠PQR = 85°. Its supplementary angle is ∠PQS = 95°. It’s external arms QR and QS lie on the straight line.
I got if the sum of measurement of two adjacent angles is 180° or 2 right angles, their external sides lie on a same straight line.
Let’s draw adjacent angles with the angles, whose measurements are given below and examine whether the external sides of those adjacent angles lie on a same straight line or not.
- 37°, 113°
- 41°, 139°
- 94°, 86°
- 90°, 90°
Question 1. Let’s think and write :
1. Whether two complementary angles are acute to each other or not.
Solution:
Two acute angles can be complementary two each other.
2. Whether two acute angles are supplementary to each other or not.
Solution:
Two acute angles cannot be supplementary to each other.
3. Let’s write whether one acute angle and one obtuse angle are complementary to each other. Also, examine whether two right angles are complementary to each other or not.
Solution:
One acute angle and one obtuse angle and two right angles cannot be complementary to each other.
4. Let’s write whether two obtuse angles are supplementary to each other or not.
Solution:
Two obtuse angles are not supplementary to each other.
5. Let’s write whether two right angles are supplementary to each other or not.
Solution:
Two right angles are not supplementary to each other.
6. Let’s write whether one acute angle and and obtuse angle are supplementary to each other or not.
Solution:
One acute angle and one obtuse angle can be supplementary to each other.
7. Whether two adjacent angles are complementary to each other.
Solution:
Whether two adjacent angles can be complementary to each other.
8. Two adjacent angles are supplementary to each other.
Solution:
Two adjacent angles can be supplementary to each other.
Question 2. Let’s draw adjacent angles with angles whose measurements are given below and examine which pair of angles are complementary to each other:
Solution:
Given
45°,45°,120°,30°,110°;42°,48°,37°,43°,85°,95°;
45°,45° – Complementary angles
70°, 110° – Supplementary angles
48°, 42° – Complementary angles
95°, 85° – Supplementary anglers
Question 3. 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°
Solution:
Given
31°,47°,64°,29°,43°,59°,17°,26°
47° and 43° – Complementary angles
64° and 26° – Complementary angles
31° and 59° – Complementary angles
Question 4. Let’s see the measurement of the angles given below and examine which pair of angles are supplementary to each other:
Solution:
47°,58°,69°,75°,133°,105°,122°,125°
47° and 133° – Supplementary angles
58° and 122° – Supplementary angles
Question 5. Let’s define adjacent angles and write which pair of angles are adjacent from the following figures :
Solution:
When two angles have a common arm, origin and both angles are on either common arm, those angles are called adjacent angles. In first and third figures ∠A and ∠B are adjacent angles.
Question 6. Let’s draw adjacent angles by protractor whose measurements are given below :
Solution:
35°,45°,18°,42°,32°,90°,73°,63°
∠ABC + ∠CBD = 35° + 45° = 80°
∠PQR + ∠RQS = 18° -4- 42° = 60°
∠XO Y + ∠YOZ = 32° + 90° =122°
∠MON + ∠NOR = 73° + 63° = 136°
Question 7. Sayantani drew a straight line AB. I erected 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 ∠PQB and ∠PQA and ∠PQB + ∠PQA by using protractor.
Solution:
Given
Sayantani drew a straight line AB. I erected a ray PQ from a point P on AB. As a result, two adjacent angles ∠PQB and ∠PQA are formed.
Question 8. Shakil draws two adjacent angles ∠ABC and ∠ABD whose sum of measurements is 180°; I also drew ∠ABC and ∠ABD like Shakil and examined whether points D, B and C lie on a same straight line or not.
Solution:
Given
Shakil draws two adjacent angles ∠ABC and ∠ABD whose sum of measurements is 180°; I also drew ∠ABC and ∠ABD like Shakil
Question 9. ∠ABC and ∠ABD are formed whose sum is 180°. We see that D, B and C lie on a same straight line.
Solution:
Given
∠ABC and ∠ABD are formed whose sum is 180°.
Let’s find the value of X from the figure beside.
∠AOD + ∠DOC+ ∠COB=180C
or, 3x° + 80° + x° = 180°
or, 4x° = 180° – 80°
or, 4x° = 100°
= \(x^{\circ}=\frac{100^{\circ}}{4}=25^{\circ}\)
The value of \(x^{\circ}=\frac{100^{\circ}}{4}=25^{\circ}\)
Question 10. From the figure if ∠AOP, ∠BOP are greater than 140°, then find the value of ∠AOP and ∠BOP.
Solution:
Given
From the figure if ∠AOP, ∠BOP are greater than 140°,
Let ∠BOP = x°
∠AOP = x° + 140°
∵ ∠AOP + ∠BOP = 180°
∴ x° + 140° + x° = 180°
or, 2x° = 180° – 140°
or, 2x° = 40°
or, x° = \(\frac{40^{\circ}}{2}\)
or, x° = 20°
∴ ∠BOP – 20° ∠AOP = 20° + 140° = 160°
Question 11. Measurement of two adjacent angles are 35°-and 145°. Let’s write how the external! sides of those two angles are situated.
Solution:
Given
Measurement of two adjacent angles are 35°-and 145°.
= 35° + 145° = 180°
∴ Both external sides of the adjacent angles lie on a same straight line.
Question 12. From the figure OA and OE line segments are situated in which manner?
Solution:
∠AOB+ ∠BOC + ∠COD+ ∠DOE
= 20° + 55° + 81°+24°
= 180°
∴ OA and OE are situated on a sama straight line.
