Hello from MrBillDoesMath!
Answer: x = 4, y = 12
Discussion:
Part One::
From Plane Geometry vertical angles are equal. This gives
6x + 10y = 18x + 6y
Subtract 6x from each sides:
10y = ( 18x - 6x) + 6y or
10y = 12x + 6y.
Subtract 6y from each side:
10y - 6y = 12x or
4y = 12x or
y = 12x/ 4 = 3x ( *)
Part Two:
A straight line has 180 degrees, which in this case becomes
(18x + 6y) + 36 = 180 or
18x + 6y = 180 -36 = 144. Dividing each side by 6 gives
3x + y = 144/6 = 24 or
y = 24 - 3x (**)
Substituting (*) into this equation gives:
3x = 24 - 3x or
6x = 24 or
x = 4 ( and y = 3x = 12)
Thank you,
MrB
