Two complementary angles have measures of 2x+5 and 3x-10. What is the measure of each of the angles?

##43^@ and 47^@##
Complementary angles are ##color(blue)2 angles whose sum is 90 degrees##
Hence ##2x + 5## and ##3x – 10## sum to ##90##.
##rArr2x+5+3x-10=90larr equation to be solved##
##rArr5x-5=90##
add 5 to both sides of the equation.
##5xcancel(-5)cancel(+5)=90+5##
##rArr5x=95##
To solve for x divide both sides by 5.
##(cancel(5) x)/cancel(5)=95/5##
##rArrx=19 is the solution##
The 2 angles are therefore.
##2x+5=(2xx19)+5=43^@##
and ##3x-10=(3xx19)-10=47^@##