RD Chapter 8 Lines and Angles Ex 8.1 Solutions
Question - 1 : - Write thecomplement of each of the following angles:
(i)200
(ii)350
(iii)900
(iv) 770
(v)300
Answer - 1 : -
(i) Thesum of an angle and its complement = 900
Therefore, the complement of 200 = 900 –200 = 700
(ii) Thesum of an angle and its complement = 900
Therefore, the complement of 35° = 90° – 35° = 55
(iii) Thesum of an angle and its complement = 900
Therefore, the complement of 900 = 900 –900 = 00
(iv) Thesum of an angle and its complement = 900
Therefore, the complement of 770 = 90° – 770 = 130
(v) Thesum of an angle and its complement = 900
Therefore, the complement of 300 = 900 –300 = 600
Question - 2 : - Write thesupplement of each of the following angles:
(i) 540
(ii) 1320
(iii) 1380
Answer - 2 : -
(i) Thesum of an angle and its supplement = 1800.
Therefore supplement of angle 540 = 1800 –540 = 1260
(ii) Thesum of an angle and its supplement = 1800.
Therefore supplement of angle 1320 = 1800 –1320 = 480
(iii) Thesum of an angle and its supplement = 1800.
Therefore supplement of angle 1380 = 1800 –1380 = 420
Question - 3 : - If an angle is 280 lessthan its complement, find its measure?
Answer - 3 : -
Let the measure of any angle is ‘ a ‘ degrees
Thus, its complement will be (90 – a) 0
So, the required angle = Complement of a – 28
a = ( 90 – a ) – 28
2a = 62
a = 31
Hence, the angle measured is 310.
Question - 4 : - If an angle is 30°more than one half of its complement, find the measure of the angle?
Answer - 4 : -
Let an angle measured by ‘ a ‘ in degrees
Thus, its complement will be (90 – a) 0
Required Angle = 300 +complement/2
a = 300 + (90 – a ) 0 / 2
a + a/2 = 300 + 450
3a/2 = 750
a = 500
Therefore, the measure of required angle is 500.
Question - 5 : - Two supplementaryangles are in the ratio 4:5. Find the angles?
Answer - 5 : -
Two supplementary angles are in the ratio 4:5.
Let us say, the angles are 4a and 5a (in degrees)
Since angle are supplementary angles;
Which implies, 4a + 5a = 1800
9a = 1800
a = 200
Therefore, 4a = 4 (20) = 800 and
5(a) = 5 (20) = 1000
Hence, required angles are 80° and 1000.
Question - 6 : - Two supplementaryangles differ by 480. Find the angles?
Answer - 6 : -
Given: Two supplementary angles differ by 480.
Consider a0 beone angle then its supplementary angle will be equal to (180 – a) 0
According to the question;
(180 – a ) – x = 48
(180 – 48 ) = 2a
132 = 2a
132/2 = a
Or a = 660
Therefore, 180 – a = 1140
Hence, the two angles are 660 and1140.
Question - 7 : - An angle is equalto 8 times its complement. Determine its measure?
Answer - 7 : -
Given: Required angle = 8 times of its complement
Consider a0 beone angle then its complementary angle will be equal to (90 – a) 0
According to the question;
a = 8 times of its complement
a = 8 ( 90 – a )
a = 720 – 8a
a + 8a = 720
9a = 720
a = 80
Therefore, the required angle is 800.