Answer:
The complement of m∠WXV is m∠UXV
Step-by-step explanation:
Complementary angles are two (or more) angles with a sum of 90 degrees.
Because line WT is dissected perpendicularly by line UX, two 90° angles are formed in ∠TXU and ∠WXU. We know that they are both 90° because of the box on ∠TXU. ∠TXU and ∠WXU are supplementary angles -- two angles that occupy the same line but are dissected by a perpendicular line forming two angles with a sum of 180 degrees.
If ∠TXU + ∠WXU = 180, and ∠TXU = 90, then ∠WXU must also equal 90:
90 + ∠WXU = 180
90 - 90 + ∠WXU = 180 - 90
0 + ∠WXU = 90
∠WXU = 90°
As we see in the diagram, ∠WXU is dissected by line SV. Because of this, it is broken into the two angles of ∠WXV and ∠UXV. We already established that ∠WXU is 90°. Therefore the sum of these two angles formed must equal 90°, which, in turn, means they are complementary angles. They complement one another.
Therefore, the complement of ∠WXV is ∠UXV