SOLUTION: two angles are complementary. one angle is ten less than three times the other angle. find the measure of both angles.

Question 647697: two angles are complementary. one angle is ten less than three times the other angle. find the measure of both angles.
Found 2 solutions by DrBeeee, shweta:
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let a = one of the angles
Let b = the other angle
Since they are complementary angles we have
(1) a + b = 90
From the statement,"one angle is 10 less than 3 times the other," we get
(2) a = 3*b - 10 (or you could use b=3a-10, it doesn't matter)
Substitute (2) into (1) and get
(3) 3*b - 10 + b = 90, or
(4) 4*b = 100, or
(5) b = 25
Then from (1) we get
(6) a = 65
Let's check these values using (2).
Is (65 = 3*25 - 10)?
Is (65 = 75 - 10)?
Is (65 = 65)? Yes
Answer: The angles are 65 degrees and 25 degrees.
Answer by shweta(56) (Show Source): You can put this solution on YOUR website!
Given :Two angles are complementary, means their sum is 90 degree.Let the two angles be a and b.
a + b = 90 degree ......(1)
It is given in the question that one angle is ten less than three times the other angle, say
b = 10 less than 3* a( 3 times 'a' means 3 multiplied by a)
b= 3*a - 10 ......(2)
Now substitute the value of 'b'in (1)
a + b = 90
a + 3*a- 10 = 90 ( coefficient of a is 1 ,so 1*a +3a= 4*a)
4*a = 90 + 10
4*a =100
a = 100/4
a = 25
One angle 'a' is 40 degrees
N ow to find the value of other angle 'b', put in the value of 'a' in the equation (2)
b= 3*a - 10
b= 3*25 - 10
b= 75- 10
b= 65 degrees

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