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

Answer:

27 and 63

Step-by-step 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

Answer:

27°,63°

Step-by-step 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 :)