Find the measures of two complementary angles if the difference in their measures is 16.

One of the angles is 53 degrees and the other is 37 degrees.

Step-by-step explanation:

Let x be equal to the measure of the first angle.

Let y be equal to the measure of the second angle.

Because x and y are complementary, they add up to 90 degrees.

x+y=90

The question tells us that x and y have a difference of 16.

x-y=16

Now that we have our two equations, we can use the method of elimination to find the value of x (process is in the picture attached). We do this by adding the two equations since y will cancel out.

x=53

Finally, we can plug x back into either of the original equations to find the value of y.

x+y=90

53+y=90

Subtract both sides by 53 to isolate y

53+y-53=90-53

y=37

I hope this helps!