Question

Analyze the diagram to complete the statements. (Picture provided)

Answer choices : greater than, less than, or equal to.

Answer 1

The answers are: Greater than, equal to, and equal to.

Explanation:

Answers: B, C, and C.

Answer 2

MXN > YZX

LZX = ZYX + YXZ

MYL = 180 - ZYX

Explanation:

The attached images show the three requested cases in order from left to right.

First case MXN is represented in orange, and YZX in green, and is evident that MXN is larger than 90 degrees, while YXZ is smaller than 90 degrees, so MXN > YXZ

Second case: LZX is represented in orange (notice also that it is equal to 180 degrees minus the angle YZX)

ZYX is represented in blue, and YXZ in green. These two angles are internal angles of the triangle XYZ, therefore, added to the triangle's third angle (YZX) should add to 180 degrees. That is:

`ZYX + YXZ + YZX = 180` therefore
`ZYX + YXZ = 180 - YZX` but this last expression exactly equal angle LZX (see statement in parenthesis above)

Third case: MYL is represented in blue, and ZYX in green

It is clear from the image that both add up to 180 degrees, therefore:

`MYL + ZYX = 180` therefore solvig for MYL:
`MYL = 180 - ZYX`

That is: both expressions are equal