SOLUTION: two angles are complementary.one angle is 42 degrees more than one half the other. find the angles.

Question 778567: two angles are complementary.one angle is 42 degrees more than one half the other. find the angles.

Found 2 solutions by stanbon, khaakenajaf:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
two angles are complementary.one angle is 42 degrees more than one half the other. find the angles.
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Equation:
x + y = 90 degrees
x = (1/2)y+42
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Substitute and solve for "y":
(1/2)y + 42 + y = 90
(3/2)y = 48
y = 32
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Solve for "x":
x = (1/2)32+42 = 16+42 = 58
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Cheers,
Stan H.
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Answer by khaakenajaf(1) (Show Source): You can put this solution on YOUR website!
Consider two angles be x and y
According to the definition of complementary angle: sum of two angles is 90 degree.
writing it in mathematical form
x + y = 90 equation (1)
Now according to the given statement:One angle is 42 degrees more than half the other
write equation (you can use the same variables)
x = 42 +1/2 y equation(2)
from equation 2 put value of x in equation 1
(x + 1/2 y) + y = 90
0.5y + y + 42 = 90
1.5 y+ 42 = 90
Subtract 42 from each side
1.5y = 48
Divide each side by 1.5 to get y alone
y = 32
Now that we know value of y (one of the two angles)
put value of y in equation 1
x + 32 = 90
x = 58
The angles are 32 degrees and 58 degrees
verification:
32 + 58 = 90
now go back to the given statemant :one angle is 42 degrees more than one half the other.
the half of 32 is 16. and 16+42=58
Q.E.D
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