1. ## Addition and Subtraction Properties

I have this one problem that I need help on, can anyone help me??

Given: Angle A is comp. to Angle B
Angle C is comp. to Angle B
Angle A = (3x + y)
Angle B = (x + 4y + 2)
Angle C = (3y - 3)

Find: Angle B

I need some help with this one, I do not understand it...
HELP!!!

2. Let's set up a system of Equations:

We know $\displaystyle m\angle A + m\angle B = 90$
and that $\displaystyle m\angle B + m\angle C = 90$ which tells us that A and C are congruent.

Now let's substitute: $\displaystyle 3x + y + x + 4y + 2 = 90$ and simplify to $\displaystyle 4x + 5y = 88$
And for our second equation $\displaystyle x + 4y + 2 + 3y - 3 = 90$ and simplify this to $\displaystyle x + 7y = 91$

Now to get x by itself $\displaystyle x = 91 - 7y$ and let's plug it into the first equation $\displaystyle 4(91 - 7y) + 5y = 88$ simplify $\displaystyle 364 - 28y + 5y = 88$ and now we get $\displaystyle -23y = -276$ and $\displaystyle y = 12$

Now just put y into the original equation $\displaystyle 4x + 5(12) = 88$ and get $\displaystyle 4x = 28, x = 7$. So now we have $\displaystyle y = 12, x = 7$

Put the values back into the original problems to see if they are true and you are done.