The angle we are looking for is $53$ degrees.
Work Step by Step
We know that complementary angles add up to $90$ degrees. Let us set one angle equal to $x$. Since the other angle is 16 degrees more than its complement, we will set this angle as $x + 16$. The equation we can use is: $$x + (x + 16) = 90$$ Distribute what is in parentheses to simplify the problem: $$x + x + 16 = 90$$ Simplify by adding the $x$ terms together: $$2x + 16 = 90$$ Subtract $16$ from both sides of the equation to isolate constants on the other side of the equation: $$2x = 74$$ Solve for $x$ by dividing both sides of the equation by $2$: $$x = 37$$ If one angle is $37$ degrees, then we can figure out the other angle is $16$ more than this angle: 2nd angle = $37 + 16$ The 2nd angle is $53$ degrees.