##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^@##