Question

The difference of two complementary angles is 40°. What are the angles?

Answer 1

`alpha = 65^@`
`beta = 25^@`

Explanation:

By definition: Two angles are Complementary when they
add up to `90^@`

so let's call the angles `alpha` and `beta`

`alpha + beta = 90^@`

`alpha - beta = 40^@`

`alpha = 40^@ + beta`

substitute:

`alpha + beta = 90^@`

`(40^@ + beta) + beta = 90^@`

`2beta = 50^@`

`beta = 25^@`

`alpha + beta = 90^@`

`alpha + 25^@= 90^@`

`alpha = 65^@`

Answer 2

One of the angles is `65˚`.
The other is `25˚`.

Explanation:

Complementary angles sum to `90˚`.

`/_1+/_2=90`

For our purposes, we will consider the first angle larger and the second angle smaller.

We are given another piece of information: that the difference of the angles is `40˚`. Difference means subtraction, so we can construct the following equation.

`/_1-/_2=40`

Now, we have two equations. There are many ways to solve this, but we will use the substitution method. Essentially, we will solve for one of the values and then plug it in to the other equation.

`/_1=40+/_2`

`(40+/_2)+/_2)=90`

Then, we need to simplify to find `/_2`.

`40+2/_2=90`

`2/_2=50`

`/_2=25`

Finally, we can plug this value back in to the original equation to find the other angle measure.

`/_1+25=90`

`/_1=65`