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^@##