Answer:
x = 28
Step-by-step explanation:
[tex] \tan(2x - 65) \degree = \cot(3x + 15) \degree \\ \\ \tan(2x - 65)\degree = \tan \{90 \degree - (3x + 15)\degree \} \\ \\ (2x - 65)\degree = \{90 \degree - (3x + 15)\degree \} \\ \\ (2x - 65)\degree + (3x + 15)\degree = 90 \degree \\ \\ (2x - 65 + 3x + 15)\degree = 90 \degree \\ \\ 5x - 50 = 90 \\ \\ 5x = 90 + 50 \\ \\ 5x = 140 \\ \\ x = \frac{140}{5} \\ \\ x = 28[/tex]
