Find x. L1 and L2 are parallel
From the image, the angles of the polygon in blue should satisfy:
6θ + 90 + 4θ + 2θ + 90 + x = 540
12θ + x = 360
x = 360 - 12θ
The Attempt at a Solution
I couldn't figure out how to advance from there so I resorted to a dirty trick using the values from the choices.
Noticing that every value of each choice is a multiply of 5 then the value of θ in the equation must be:
θ = 5n
So it follows that:
x = 360-12(5n)
Then by trial and error:
x = 180 for n = 3
x = 120 for n = 4
x = 60 for n = 5
From the image x should be obtuse so then I conclude that x must be equal to 120
and the answer would be the letter 'b'. I know I got it right cause my book says that's the correct answer. However since this is a section of my book were no development of the solution is presented (just the final answer) I'm asking for some tips on other methods to solve this. Perhaps I'm overlooking something...
Thanks in advance.