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TiffanyReynolds3
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Geometry Guide (p.131/Lines and Angles)

by TiffanyReynolds3 Tue Dec 02, 2014 11:25 am

In the 4th ed. Geometry Guide (p.131/Lines and Angles),
#12 (see diagram)

b=4x, e = x+ 2y, d=3y+8

The lines are parallel and therefore, e=d. I see the solution as being solved using systems of equations. I am going back through my work so see where I went wrong.

Since a and b are supplementary, they add up to 180.

b= 4x, therefore, a = 180 – 4x, or 45 – X. d = a = h = 45 – X
X is solvable for 28 using system of equations, which would make h = 17 (since 45-28=17). However, h= 68.

Where is the error in my calculation/solution?
n00bpron00bpron00b
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Re: Geometry Guide (p.131/Lines and Angles)

by n00bpron00bpron00b Tue Dec 02, 2014 12:36 pm

given b=4x, e=x+2y, d=3y+8

as you said "a" and "b" are supplementary, they add up to 180

we are given b=4x :: "a" will be 180-4x (a+b = 180)

Now,

"a" = "d'.

Be careful the value of "d" will not be just 180-4x (same applies to "h" ; the value of "h" is not just 180-4x). A specific value for "d" and "e" has already been assigned in the problem statement.


d=3y+8 - given

Using the given value of "d" and knowing that "a" = "d",
3y + 8 = 180-4x
d = 4x + 3y = 172 - (1)

Similarly,

we know that "a" is equal to "e" - corresponding angles
a = 180 - 4x
e = x + 2y (given)

a = e

The value of "e" will be

x + 2y = 180 - 4x
5x + 2y = 180

Now,

"e" = "h" (vertically opposite angles)

h = 5x + 2y = 180 - (2)

Solving equation (1) and (2) gives us
x=28
y = 20

b = 4x = 4 * 28 = 112
b + d = 180 (supplementary angles)
so d = 180 - 112
d = 68

Also,
d=h (corresponding angles)
h = 68

the above method is very time consuming, instead we could just make use of the given information to get to the solution faster.

b = 4x
d = 3y + 8

b+d=180
4x + 3y + 8 = 180
4x + 3y = 172 - (1)

also, e = d

x + 2y = 3y + 8
x - y = 8 - (2)

Solving (1) & (2)

x = 28
y = 20

plugging in the value for x and y ..we get h = 68
tommywallach
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Re: Geometry Guide (p.131/Lines and Angles)

by tommywallach Tue Dec 02, 2014 9:26 pm

Noob's final explanation here is definitely the winner, but man that sure was comprehensive! : )

-t