Question

Which relationship is always true for the angles r, x, y, and z of triangle ABC?

x + z = y

180 degrees − x = r

x + y + z = 180 degrees

x + y + z = 90 degrees

Answer 1

we know the 3 angles of a triangle add up to 180, so one possible answer is
x+y+r= 180

but they did not give us that option.

Answer 2

we could think some more. we also know a straight line make 180 degrees
in other words, we can write
x+r = 180

Answer 3

Or 180 - x = r?

Answer 4

It would help if I used the right angles
we know the 3 angles of a triangle add up to 180, so one possible answer is

z+y+r= 180

Answer 5

one thought is to set the two equations equal to each other
if
z+y+r= 180
and
x+r = 180
then
z+y+r=x+r

Answer 6

I see

Answer 7

we can simplify that last equation
z+y+r=x+r

by adding -r to both sides.

Answer 8

so, it could be. z+y+r=x+r=180-x=r?

Answer 9

I was not looking at the choices, but that last equation simplifies to
z+y = x
which is also not a choice.

But you found the choice already, from
r+x= 180
r= 180 - x

Answer 10

Thank you for the help, I have been struggling in this particular subject in math, it helps me alot. :)

Answer 11

just to be clear

r+x = 180
add -r to both sides
r -r + x = 180 -r
and on the left side r-r is 0 and 0+x is x, so we get
x= 180-r

Answer 12

Ok, thanks again.

Answer 13

yw