measure of angle?

Question

i need help with this problem:

find the measure of angle T if the measure of angle T is 20 more than four times its supplement.

i'm not sure how i can set it up...


-thanks :)

Answer 1

T + T's supplement = 180 degrees so T's supplement = 180 - T

T = 20 + 4(180 - T)
T = 20 + 720 - 4T
5T = 740
T = 148 degrees

Answer 2

First off, let me tell you what supplementary angles are. Also, the symbol that I'm going to be using, θ, means "angle" in mathematics.

Supplementary angles: Two angles adjacent to each other whose sum is equal to 180º.
Alright, now knowing this, let's look at the problem.
Now, θT is 20 more than four times its supplement. It's supplement is logically 180º - θT, because if you subtract this angle from 180º, you will get the other angle that, when added to θT, equals 180º.
So, let's set the problem up like this:

θT= 4(180º - θT) + 20

Now, we want to figure out the value of θT. The easiest step to start with would be to use the distributive propert on 4(180º - θT).

Distributive property: For any numbers x, y and z, x(y+z)=xy+xz.

So let's use the distributive property to simplify this problem.

4(180º - θT) = 720º - 4θT

Now, substituting the new representation of the value of the above into the equation, we get:

θT = 720º- 4θT + 20º

Now, since we're trying to solve for θT, we should put all of the θT terms on one side of the equation. We have to add 4θT to both sides of the equation. This cancels out the -4θT on the right side of the equation. Also, what you do to one side of the equation you have to do to the other to keep it equal, logically. Doing this, we get:

5θT = 720º + 20º

Now we add both of the angle measures together on the right side of the equation and obtain:

5θT = 740º

Now, logically, we divide both sides by five. This isolates θT and gives us the value of it:

(5θT)/5 = (740º)/5

θT = 148º

Therefore, your answer is:

θT = 148º

There you go, I'm glad I could help. :)

Answer 3

Supplement of T = 180 -T
So T = 4(180-T) + 20
T= 720-4T +20
5T = 740
T = 148