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