Question

if ( mangle rxu = 128^{circ} ), then what is ( mangle txs )?

Explanation:

Step1: Find the measure of $\angle 2$

Since $\angle RXU$ and $\angle 2$ are supplementary angles (they form a linear - pair), and the sum of supplementary angles is $180^{\circ}$.
If $m\angle RXU = 128^{\circ}$, then $m\angle 2=180^{\circ}-m\angle RXU$.
So, $m\angle 2 = 180^{\circ}-128^{\circ}=52^{\circ}$.

Step2: Use the vertical - angle relationship

$\angle TXS$ and $\angle 2$ are vertical angles. Vertical angles are congruent (have equal measures).

Answer:

$52^{\circ}$