Question 605977: two supplementary angles are in the ratio 7:2 how many degrees are there in the measure of the larger angle? Answer by Sarey(4) (Show Source):
You can put this solution on YOUR website! (1)
Let x - no of degrees in the smaller angle
Therefore 2x the no of degrees in the larger angle
Therefore 2x + x = 180 and hence x = 60 degrees and the greater angle is 2*60 = 120 deg.
(2)
180 = x + (x - 20) = 2x - 20
2x = 200
x = 100
Thus 100 is one angle and 80 is the second angle
80 deg is the answer to your question.
(3)
7x + 2x = 180
9x = 180
x = 20
One angle is 7*20 = 140 deg
The other angle is 2*20 = 40 deg
and 140 + 40 = 180 deg
(4)
(3a + 10) + (2a - 40) = 5a - 30 = 180
and 5a = 180 + 30 = 210
a = 42
The angles are 3*42 + 10 = 126 + 10 = 136 deg
and 2*42 - 40 = 84 - 40 = 44 deg
Add the angles 136 + 44 = 180
The smaller angle is 44 degrees
(5)
Let the measure of the angle you seek be 'x'
2x = twice the angle
The angle which is 60 more than twice the angle = {60 + 2x}
Therefore x + {60 +2x} = 180
3x + 60 =180
3x = 120
x = 40 deg is the answer;
check 2*40 = 80
2*40 + 60 = 140
and 40 + 140 = 180 ok
(6)
Let x = one angle
Let x + 80 the other angle
Thus x + {x + 80} = 2x + 80 = 180
2x = 100
x = 50
Thus one angle = 50 and
the other angle = 130 deg which is the answer
(7)
Let the sought angle be 'x' and its supplement is {180 - x}
The compliment of 'x' is {90 - x}
We are told that {180 - x} - 5*{90 - x} = 10
180 - x - 450 + 5x = 10
4x = 10 + 450 - 180 = 460 - 180 = 280
x = 70 degrees which is the answer to the question
Check
supplement = 180 - 70 = 110
compliment = 90 - 70 = 20
Five times the compliment = 5*20 = 100
supplement - 5*compliment =
110 - 100 = 10 ok
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