Question

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

Answer 1

`2x + 5 = 43^@`
`3x - 10 = 47^@`

Explanation:

A complementary angles means angles that add up to `90` degrees. The two angles given in the question are complementary angles.
So
Our first angle `(2x+5)` plus the second angle `(3x-10)` is equal to `90` degrees
`(2x+5) + (3x-10) = 90`
Now we solve for `x`, first we add up the like terms
`2x + 3x + 5 - 10 = 90`
`5x - 5 = 90`
Add `5` to both sides
`5x = 95`
Divide both sides by `5` we get
`x = 19`
Now and after we find `x` we substitute it to get our two angles
`2x + 5 = 2(19) + 5 = 43^@`
`3x - 10 = 3 (19) - 10 = 47^@`
Hope it helps :)

Answer 2

`43^@" and " 47^@`

Explanation:

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^@`