Question

Darnelle drew this figure and the accompanying equations.

w + x + y = 180 y + z = 180Which equation must also be true?
A
w + z = 180
B
y – x = w
C
w + x + z = 180
D
w + x = z

Answer 1

180=w+x+y and 180=y+z so

w+x+y=z+y so subtract y from both sides

w+x=z

Answer 2

The correct option is D w + x = z

Explanation:

Consider the provided equations.

`y + z = 180`

Solve the equation for y.

`y= 180-z`

Now substitute the vlaue of y in
`w + x + y = 180`

`w + x + 180-z = 180`

Subtract 180 from both sides.

`w + x + 180-180-z = 180-180`

`w + x -z = 0`

Add z to both sides.

`w + x -z+z = z`

`w + x= z`

Hence, the correct option is D w + x = z