Questions on Geometry: Angles, complementary, supplementary angles answered by real tutors!

Algebra ->  Algebra -> Questions on Geometry: Angles, complementary, supplementary angles answered by real tutors!     (Log On)
Ad: Algebra Solved!™: algebra software that solves YOUR algebra homework problems with step-by-step help!


Question 146556: an angle of x degree has property that its complement is equal to 1/6 of its supplement.: an angle of x degree has property that its complement is equal to 1/6 of its supplement.
Answer by Alan3354(1934) About Me  (Show Source):
You can put this solution on YOUR website!
an angle of x degree has property that its complement is equal to 1/6 of its supplement.
Call the angle A.
The complement is 90-A, and the supplement is 180-A.
So, 180-A = 6(90-A)
180-A = 540-6A
5A = 360
A = 72 degrees
The complement is 18, and the supplement is 108.
Question 146556: an angle of x degree has property that its complement is equal to 1/6 of its supplement.: an angle of x degree has property that its complement is equal to 1/6 of its supplement.
Answer by MathLover1(1160) About Me  (Show Source):
You can put this solution on YOUR website!
definitions:
Complementary Angles: Two angles that add up to 90°
Supplementary Angles: Two angles that add up to 180°

Given:
an angle of x degree
let its complement be y degree
let its supplement be z degree

so, we have the system:
x+y=90 …………(1)
x+z=180………….(2)

if its complement y is equal to 1/6 of its supplement, we will have:
y=1/6(z)
x+y=90 …………substitute y with 1/6(z)
x+1/6(z)=90…multiply both sides by 6
6x+z=540………solve for z
z=540-6x……….substitute into (2)
x+z=180………….(2)
x+540-6x =180
540-5x =180
540-180 =5x
360=5x
x =72……….the angle

z=540-6x
z=540-6(72)
z=540- 432
z= 108………… its supplement

x+y=90 …………(1)
y=90- x
y=90- 72
y=18……….. its complement

check:
its complement y is equal to 1/6 of its supplement:
y=1/6(z)
18=1/6(108)
18=18