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)┬аThesum of an angle and its complement = 900
Therefore, the complement of 200┬а= 900┬атАУ200┬а= 700
(ii)┬аThesum of an angle and its complement = 900
Therefore, the complement of 35┬░ = 90┬░ тАУ 35┬░ = 55
(iii)┬аThesum of an angle and its complement = 900
Therefore, the complement of 900┬а= 900┬атАУ900┬а= 00
(iv)┬аThesum of an angle and its complement = 900
Therefore, the complement of 770┬а= 90┬░ тАУ 770┬а= 130
(v)┬аThesum of an angle and its complement = 900
Therefore, the complement of 300┬а= 900┬атАУ300┬а= 600
Question - 2 : - Write thesupplement of each of the following angles:
(i) 540
(ii) 1320
(iii) 1380
Answer - 2 : -
(i)┬аThesum of an angle and its supplement = 1800.
Therefore supplement of angle 540┬а= 1800┬атАУ540┬а= 1260
(ii)┬аThesum of an angle and its supplement = 1800.
Therefore supplement of angle 1320┬а= 1800┬атАУ1320┬а= 480
(iii)┬аThesum of an angle and its supplement = 1800.
Therefore supplement of angle 1380┬а= 1800┬атАУ1380┬а= 420
Question - 3 : - If an angle is 280┬аlessthan its complement, find its measure?
Answer - 3 : -
Let the measure of any angle is тАШ a тАШ degrees
Thus, its complement will be (90 тАУ a)┬а0
So, the required angle = Complement of a тАУ 28
a = ( 90 тАУ a ) тАУ 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 тАШ a тАШ in degrees
Thus, its complement will be (90 тАУ a)┬а0
Required Angle = 300┬а+complement/2
a = 300┬а+ (90 тАУ a )┬а0┬а/ 2
a + a/2 = 300┬а+ 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┬аand
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┬аbeone angle then its supplementary angle will be equal to (180 тАУ a)┬а0
According to the question;
(180 тАУ a ) тАУ x = 48
(180 тАУ 48 ) = 2a
132 = 2a
132/2 = a
Or a = 660
Therefore, 180 тАУ a = 1140
Hence, the two angles are 660┬аand1140.
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┬аbeone angle then its complementary angle will be equal to (90 тАУ a)┬а0
According to the question;
a = 8 times of its complement
a = 8 ( 90 тАУ a )
a = 720 тАУ 8a
a + 8a = 720
9a = 720
a = 80
Therefore, the required angle is 800.