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

Answer:

D. x + y = w

Step-by-step 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.