Question 162875
Let the angle you want to find = A.
The supplement of angle A is {{{(180-A)}}}.
Half the supplement of angle A is {{{(1/2)(180-A)}}}
The complement of angle A is {{{(90-A)}}}.
Twice the complement of angle A is {{{2(90-A)}}} and 12 degrees less than that is {{{2(90-A)-12}}}.
Now let's put it all together as described in the problem statement!
{{{(1/2)(180-A) = 2(90-A)-12}}} Now we can solve for the unknown angle A. First, multiply both sides of this equation by 2 to clear the fraction.
{{{(180-A) = 4(90-A)-24}}} Expand (distributive property) the right-hand side.
{{{180-A = 360-4A-24}}} Simplify.
{{{180-A = 336-4A}}} Add A to both sides.
{{{180 = 336-3A}}} Subtract 336 from both sides.
{{{-156 = -3A}}} Finally, divide both sides by -3.
{{{52 = A}}}
The measure of the angle A is 52 degrees.