Haryana Board Class 8 Maths Solutions For Chapter 2 Complementary Angles, Supplementary Angles, And Adjacent Angles
Question 1. Find the measurement of Complementary angles of 38.5°, \(33 \frac{2}{3}^{\circ}\), 90°.
Solution:
The measurement of the Complementary angle of 38.5°, (90°-38.5°) or 51.5°.
The Complementary angle of \(33 \frac{2}{3}^{\circ}\) is (90° – \(33 \frac{2}{3}^{\circ}\)) or \(56 \frac{1}{3}^{\circ}\)
The Complementary angle of 90° is (90°-90°) or 0.
Question 2. Find the measurement of Supplementary angles of 120°, 0°, 128.6°, 90°.
Solution:
The measurement of the Supplementary angle of 120° is (180°-120°) or 60°.
The Supplementary angle of 0° is (180°-0°) or 180°
The Supplementary angle of 128.6° is (180°- 128.6°) or 51.4°
The Supplementary angle of 90° is (180°-90°) or 90°
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Question 3. Which pair of angles are complementary?
- 52°, 48°
- x°, 90°-x°,
- 60°, 120°.
Solution:
52°+48° = 100°
x°+90°-x° = 90° [complementary angles]
60°+128° = 180°
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Question 4. Which pair of angles are Supplementary?
- 42°, 139°
- 70°, 110°,
- 90°, 90°
Solution:
42°+1839° = 181°
70° +110° = 180° – Supplementary angles
90+90= 180° – Supplementary angles
Verification of the Relation Between Angles and Sides of a Triangle Class 8
Question 5. If measurements of two adjacent angles are 85.4° and 94.6%, then how external sides of those two angles are Situated?
Solution:
The Sum of two adjacent angles is 85.4°+ 94.6° = 180°
So, the external sides of the two angles are situated on the Same Straight line.
Question 6. A and B are Supplementary angles to each other. If ∠A = (x + 20)°, then find the value of ∠B.
Solution:
∠A and ∠B are Supplementary angles.
∠A + ∠B = 180
(x+20°) + ∠B = 180°
∠B = 180°- x° – 20°
∴ ∠B = (160-x)°
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Question 7. If one angle of the Complementary angle is u times the Other then find the measurement of the Smaller angle.
Solution:
Let the measurement of the Smaller angle be x.
∴ The other angle is 4x°
⇒ 4x°+2°-90°
⇒ 5x° = 90°
⇒ \(x^{\circ}=\frac{90^{\circ}}{5}\)
⇒ x°= 18°
The measurement of the Smaller angle is 18°.
Question 8. Find the Complementary and Supplementary angles of 72°13′24′′.
Solution:
The Complementary angle of 72° 13’24” is (90-72°13’24”)
⇒ \(\begin{aligned}
& 90^{\circ}=89^{\circ} 59^{\prime} 60^{\prime \prime} \\
&\quad \quad-72^{\circ} 13^{\prime} 24^{\prime \prime} \\
& \hline \quad \quad \quad 17^{\circ} 46^{\prime} 36^{\prime \prime} \\
& \hline
\end{aligned}\)
= 17°46’36”
The Supplementary angle of 72°13′24′′ is (180°-72°13′24′′)
⇒ \(\begin{aligned}
& 180^{\circ}=179^{\circ} 59^{\prime} 60^{\prime \prime} \\
&\quad \quad -72^{\circ} 13^{\prime} 24^{\prime \prime} \\
& \hline \quad \quad \quad 107^{\circ} 46^{\prime} 36^{\prime \prime} \\
& \hline
\end{aligned}\)
= 107°46’36”
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Question 9. In the adjacent figure, how are the line Segment OA and OE situated?
Solution:
∠AOF = ∠AOB + ∠BOC+ ∠COD + ∠DOE + ∠EOF
= 25° + 32° + 41°+ 40°+ 42° = 180° (one Straight line)
∴ OA and OF are on the Same straight line.
Question 10. Find the measurements of complementary and Supplementary angles of (2x-15)°
Solution:
The Complementary angles of (2x-15)° is (90-2x+15)° Or (105-2x)° and Supplementary angles is (180°-2x-+15)° or (195-2x)°.
Question 11. Choose the Correct answer:
1. The Complementary angle of 90° is
- 90°
- 45°
- 0°
- None of these.
Solution: (90°-90°) = 0°
The Correct answer is (3).
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2. The Supplementary angle of 45° is
- 90°
- 135°
- 0°
- 45°
Solution:
(180°-45°) = 135°
The Correct answer is (2)
3. Which pair of angles are not Supplementary?
- 42°, 139°
- 70°, 110°
- 90°, 90°
- x, 180°-x°
Solution:
42°+139° = 181°
70+110° = 180° – Supplementary angle
90°-+90° = 180° – Supplementary angle
X+180x = 180° – Supplementary angle
The Correct answer is (1)
Question 12. Write ‘True’ or ‘False’.
1. Any two adjacent angles are Complementary to each other.
Solution:
If the Sum of measurements of two angles is equal to 90°, then each angle is Called Complementary to the other angle.
The sum of any two adjacent angles maybe 90° or may not be 90°
So the statement is false.
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2. The Supplementary angle of the right angle is a right angle.
Solution:
The Supplementary angle of the right angle is (180°-90°) or 90° which is a right angle.
So the statement is true.
Question 13. Fill in the blanks are not _________ to each other.
1. Two acute angles
Solution: Supplementary.
2. The Complementary angle of x° is
Solution: 90°-x°