Question

two complementary angles have a difference of 36°. Find the measure of each angle. (Complementary angles are angles that add up to 90°) Show ur work

Answer 1

27 and 63

Explanation:

x - y = 36

x + y = 90

add the equations together

2x = 126

x = 63

substitute x for x in the first equation

63 - y = 36

y = 27

Answer 2

27°,63°

Explanation:

Let the two angles be a and b.

They are complementary, meaning they add up to 90. Thus:

`a+b=90`

And we are told their difference is 36. Therefore:

`a-b=36`

Solve for the system of equations. Add b to both sides in the second equation:

`a=b+36`

Substitute this into the first:

`(b+36)+b=90`

Combine like terms;

`2b+36=90`

Subtract 36:

`2b=54`

Divide by 2:

`b=27`

So, b is 27 degrees.

Use the second equation again:

`a-b=36`

Now that we know b is 27, substitute:

`a-27=36`

Add 27 to both sides:

`a=63`

So, a is 63 degrees.

And we're done :)