Tan 2x - cot x = 0
2tan x / (1 - tan^2 x) - 1/tan x = 0
2tan^2 x - (1 - tan^2 x) = 0
2tan^2 x - 1 + tan^2 x = 0
3tan^2 x - 1 = 0
tan^2 x = 1/3
tan x = + or - 1/√3
The measure of angle 1 would be (3x+2) and the measure of angle 2 would be (5x+10). There is no way to determine the exact degrees of these angles because not enough information is given.
The vertex for this function would be (-2,-79)