Question 471065
 Let the obtuse angle be = x
 Let the acute angle be = y

  x + y = 160   .......   ........        (1)
  {{{((180-x)/(2))+(90-y) = 75}}}
  {{{90-(x)/(2)+ 90-y = 75}}}
  {{{180 - 75 = (x)/(2) + y}}}
  {{{105 = (x)/(2) + y}}}   .........   ........Multiplying both the sides by 2, we get:
  {{{x + 2y = 210}}}  ........  ........   (2)
  From Eqn.(2) - (1) we get,
  {{{y = 50}}}
  Applying y's value in Eqn.(1), we get
  x + 50 = 160;  So,  x = 160 - 50 = 110.

  So, the measure of obtuse angle = 110 ;
  and the measure of acute angle = 50.    Answer.
  
  I hope you have understood the above solution.  All the best.

gsm