The question that I'm having issues with is, "The complement of an angle, A, in degrees, is equal to one-sixth of the supplement of the angle, also in degrees. Then A= "I know the answer is 72 degrees, but I don't know how to figure the problem out!
Answers
Answer 1
Answer:
'Complement' = difference between an angle an 90 degrees.
'Supplement' = difference between an angle and 180 degrees.
Complement of A = 90 - A
Supplement of A = 180 - A
The problem says that the complement is 1/6 of the supplement, right ?
So 90 - A = (1/6) x (180 - A)
Multiply each side of this equation by 6 :
540 - 6 A = 180 - A
Subtract 180 from each side:
360 - 6 A = - A
Add 6A to each side :
360 = 5 A
Divide each side by 5 :
A = 72°
'Supplement' = difference between an angle and 180 degrees.
Complement of A = 90 - A
Supplement of A = 180 - A
The problem says that the complement is 1/6 of the supplement, right ?
So 90 - A = (1/6) x (180 - A)
Multiply each side of this equation by 6 :
540 - 6 A = 180 - A
Subtract 180 from each side:
360 - 6 A = - A
Add 6A to each side :
360 = 5 A
Divide each side by 5 :
A = 72°
Answer 2
Answer:
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r = diameter/2 = 12 / 2 = 6 inches.
h = 10
V = πr²h
V = π * 3² * 6 = π*9*6 = 54π
Volume = 54π cubic inches
Assuming π ≈ 3.14159
V = 54π ≈ 54 * 3.14159 ≈ 169.64586
Volume V = 54π in³ or ≈ 169.65 in³
I hope this helped.
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