Question

Which of the following statements is true about this diagram? Check all that apply.

A. x + y = z
B. w > y
C. w > x
D. x + y = w
E. y + z = w
F. z > x

Answer 1

B) w is greater than y
C) w is greater than x

Answer 2

D. x + y = w

Explanation:

From the image, we observe that
`\angle X, \angle Y, \angle Z` are internal angles of the triangle.

So, they are internal angles then,

`\angle X+ \angle Y+ \angle Z=180\°`

Now, from the image we observe that
`\angle w` is adjacent to
`\angle Z` and both must sum 180°, because they are on a straight angle, so

`\angle w +\angle Z=180\°`

Then, we replace the second equation into the first one

`\angle X +\angle Y +\angle Z=\angle w + \angle Z\\\angle X +\angle Y=\angle w`

Therfore, the right statement is D, because the sume of angles X and Y are equal to angle W.