# how to find the complement and supplement for a variable?

#### melissa12

##### New member
How would you find the complement and supplement for a variable? For example. I have to find it for the variable Z. How would I do that? I know how to use the formula, but I am not sure what to do, since it is a variable.

#### Subhotosh Khan

##### Super Moderator
Staff member
How would you find the complement and supplement for a variable? For example. I have to find it for the variable Z. How would I do that? I know how to use the formula, but I am not sure what to do, since it is a variable.
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

#### Dr.Peterson

##### Elite Member
I presume the variable represents an angle; is it in degrees or in radians?

It will help if you show the context (the whole problem for which you need to do this, and its instructions); and also the formula you are referring to. You should be able to use the variable in it just as well as a number! You may be overcomplicating it.

#### melissa12

##### New member
I presume the variable represents an angle; is it in degrees or in radians?

It will help if you show the context (the whole problem for which you need to do this, and its instructions); and also the formula you are referring to. You should be able to use the variable in it just as well as a number! You may be overcomplicating it.
Yes, it is in degrees. So, the problem is asking for the complement and the supplement. The formula for complement is x + y = 90° and the formula for supplement is x + y = 180°. The problem wants me to find the complement and supplement for Z°. There is no picture or angle to go with the problem, you just have to solve it. I know that Z° is supposed to go in the spot of x, but I don‘t know what to do next.

#### melissa12

##### New member
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

Well, I tried to put it in the formulas x + y = 90° and x + y = 180°, but I am not sure what to do next since i am just stuck on Z° + y = 90°

#### Subhotosh Khan

##### Super Moderator
Staff member
Well, I tried to put it in the formulas x + y = 90° and x + y = 180°, but I am not sure what to do next since i am just stuck on Z° + y = 90°
For us to be able to help you properly, you need to post the COMPLETE problem statement.

#### melissa12

##### New member
For us to be able to help you properly, you need to post the COMPLETE problem statement.
OK, the problem is asking for the complement and supplement of <M which equals Z°.

#### Dr.Peterson

##### Elite Member
Yes, it is in degrees. So, the problem is asking for the complement and the supplement. The formula for complement is x + y = 90° and the formula for supplement is x + y = 180°. The problem wants me to find the complement and supplement for Z°. There is no picture or angle to go with the problem, you just have to solve it. I know that Z° is supposed to go in the spot of x, but I don‘t know what to do next.
My guess is that you don't have a lot of experience using variables, so you are expecting something harder than it is. I'll take you through the first part.

Suppose you were asked for the complement of 20 degrees. I think you are saying that you would write 20 + y = 90 and solve by subtracting 20 from both sides, to get y = 70°.

Now you are asked for the complement of z degrees. Do the same thing with z that you did with 20: Write z + y = 90, and solve for y by subtracting z from both sides: y = 90 - z. That is the answer! When you are given a variable rather than a number, the result will be an expression rather than a number, and that is all that is expected.

In fact, what we've done is to find a formula for the complement, in the sense of an equation that directly gives you the number when you plug in a value. The formula is that the complement of z degrees is y = 90 - z degrees. Now if I gave you an angle, such as 20 degrees, you can just plug that in place of z, and say that the complement is y = 90 - 20 = 70, as we already saw. That is the benefit of using variables: We can do the algebra once, and then just have to do arithmetic (evaluating an expression) to solve any specific problem of that type.

Now, can you do the part about the supplement?

• melissa12

#### Subhotosh Khan

##### Super Moderator
Staff member
OK, the problem is asking for the complement and supplement of <M which equals Z°.
That is not good enough (at least for me).

What is the EXACT problem statement (without your interpretation of "what it is asking" for)?

#### melissa12

##### New member
My guess is that you don't have a lot of experience using variables, so you are expecting something harder than it is. I'll take you through the first part.

Suppose you were asked for the complement of 20 degrees. I think you are saying that you would write 20 + y = 90 and solve by subtracting 20 from both sides, to get y = 70°.

Now you are asked for the complement of z degrees. Do the same thing with z that you did with 20: Write z + y = 90, and solve for y by subtracting z from both sides: y = 90 - z. That is the answer! When you are given a variable rather than a number, the result will be an expression rather than a number, and that is all that is expected.

In fact, what we've done is to find a formula for the complement, in the sense of an equation that directly gives you the number when you plug in a value. The formula is that the complement of z degrees is y = 90 - z degrees. Now if I gave you an angle, such as 20 degrees, you can just plug that in place of z, and say that the complement is y = 90 - 20 = 70, as we already saw. That is the benefit of using variables: We can do the algebra once, and then just have to do arithmetic (evaluating an expression) to solve any specific problem of that type.

Now, can you do the part about the supplement?
Thank you!! Yes I was struggling on this one because I am not that good at doing variables especially new things. Would the supplement be y = 180 - z?

#### melissa12

##### New member
That is not good enough (at least for me).

What is the EXACT problem statement (without your interpretation of "what it is asking" for)?
Well...It is one question of out many in a batch, so.. the exact problem would be “<M = Z°” and instructions out of all are “Find the measures of the complement and the supplement of <M.”

#### Dr.Peterson

##### Elite Member
Thank you!! Yes I was struggling on this one because I am not that good at doing variables especially new things. Would the supplement be y = 180 - z?
Yes. I would consider this to be the "formula" for the supplement of an angle; when you think "supplement", you can just think "180 - __".