Question

(02.07)Which relationship is always true for the angles x, y, and z

(IGNORE THE RED R)


http://assets.openstudy.com/updates/attachments/556e18efe4b0c4e453fa5562-keshaun45-1433278729503-untitled.png

x + z = y
y + z = x
x + y + z = 180 degrees
x + y + z = 90 degrees

Answer 1

For a solid fact, I know it isn't 180 degrees

Answer 2

@phi

Answer 3

x is an "exterior angle"

we know the 3 angles inside the triangle add up to what ?

Answer 4

180 @phi

Answer 5

in other words, using the labels in your figure
r+y+z= 180

next, any idea what r and x add up to ? (It looks like a straight line to me)

Answer 6

r + x = 180?...

Answer 7

yes, so using algebra
r= 180-x

if we use that in
r+y+z= 180
i.e. replace r with 180-x we get

180-x + y+z = 180

add -180 to both sides
-x + y+z=0
add x to both sides
y+z=x
or
x= y+z

people memorize this result: the exterior angle equals the sum of the two "non-adjacent" interior angles.