Question

The measures of 2 angles of a triangle are given. Find the measure of the 3rd angle. Show and explain work.

34. x degree , y degree
36. c degree , (2c + 1) degree

My Answers: Check to see if correct. If not, explain why in detail.

34. 180 - x - y
36. (179 - 3c) degrees

Answer 1

The sum of the angles is 180. If you know two x and y. What would be the thrid one z?

Answer 2

Are you here?

Answer 3

cause a triangle has 3 sides & 3 angles so if it already has given you a x and a y then what would the last angle be oh z would be the last angle. In addition to, the sum of the measures of the angles in any triangle is 180 degrees. @eliesaab

Answer 4

Oh and knowing 2 angles you can clearly get the 3rd angle

Answer 5

@zepdrix help hehe

Answer 6

Ya I saw you working on this one earlier I think.

You have the right idea that three angles of a triangle give us 180 degrees.

\(\large\rm x + y + \color{orangered}{z} = 180\)

But what they're asking for is...
given that you already know information about x and y,
solve for \(\large\rm \color{orangered}{z}\).

They want you to isolate that angle.

Answer 7

For example if x=10 and y=20,\[\large\rm 10+20+z=180\]How would we figure out this last angle?
Well we would do the algebra steps that we're familiar with in order to get our variable alone. So in this example we would start by subtracting 10 from each side,\[\large\rm 20+z=180-10\]And continue by subtracting 20 from each side,\[\large\rm z=180-10-20\]Yay we did it!
We solved for our third angle in this example I made up,\[\large\rm z=150\]

Answer 8

If angle x is not given to be 10, but instead just... x,
then we would have to subtract x from each side, instead of 10, right?

Answer 9

so would it be: y = 180 - x

Answer 10

180 - x - y

Answer 11

Ah that looks better!
Isolating the value of your third angle, denoted by the letter z,\[\large\rm z=180-x-y\]So yes, that's your answer to 34,
180-x-y.

That entire calculation is the value of the missing angle.

Answer 12

could the answer be z = 180 - x - y

Answer 13

Sure, as long as it's clear that you're using z for the third angle.
If you were putting this into an online assignment though, you would only enter the 180-x-y portion of it.

Answer 14

okay makes it little more clearer. What about 36?

Answer 15

So in this next one, we have our three angles being \(\rm c\), \(\rm 2c+1\), and \(\rm z\).

So then,
\(\large\rm c+2c+1+z=180\)

Answer 16

Same steps as last time, we want to isolate the letter z.
This one might take one extra calculation since we have the +1.

Answer 17

I'm starting by adding the three angles together to get 180 degrees.
c+(2c+1)+z
They should sum to 180.
c+(2c+1)+z = 180

The brackets can be dropped,
c+2c+1+z = 180
I just put those there to distinguish between the 1st 2nd and 3rd angles.
Maybe combine like-terms before doing any subtraction.

c+2c = ?

Answer 18

c + 2c = 3c of course hehe! :D

Answer 19

\[\large\rm \color{royalblue}{c+2c}+1+z=180\]Ok good,\[\large\rm \color{royalblue}{3c}+1+z=180\]

Answer 20

Try to apply the same steps you used in the last problem.
You will probably catch the mistake in the solution you listed above.

Answer 21

I would subtract 1 from sides first

Answer 22

then I would subtract 3c from both sides so z = 179 - 3c

Answer 23

Yay good job!

Answer 24

yes finally learning something lol! :D

Answer 25

lol :3