Question 83462
Let the measure of the required angle be x.
One half the complement of x is {{{(1/2)(90-x)}}} and three fourths of the supplement of x is{{{(3/4)(180-x)}}} The sum of thease is 110 degrees, so...
{{{(1/2)(90-x)+(3/4)(180-x) = 110}}} Simplify and solve for x. Multiply through by 4 to clear the fractions.
{{{2(90-x)+3(180-x) = 4(110)}}} Expand.
{{{180-2x+540-3x = 440}}} Combine like-terms.
{{{720-5x = 440}}} Subtract 720 from both sides.
{{{-5x = -280}}} Divide both sides by -5.
{{{x = 56}}}degrees.

Check:
{{{(1/2)(90-56)+(3/4)(180-56) = (1/2)(34)+(3/4)(124)}}} = {{{17+93 = 110}}} OK!