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Consider three lines as follows. L1:5x-...

Consider three lines as follows. `L_1:5x-y+4=0` `L_2:3x-y+5=0` `L_3: x+y+8=0` If these lines enclose a triangle `A B C` and the sum of the squares of the tangent to the interior angles can be expressed in the form `p/q ,` where `pa n dq` are relatively prime numbers, then the value of `p+q` is (a)`500` (b)` 450 ` (c)` 230` (d) ` 465`

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