Given that $m\angle RSW = m\angle TSU$ and $m\angle RST = m\angle WSU$, we need to prove that $m\angle RST = m\angle WSU$. Note that the problem statement already has the prove statement written out, so we are probably trying to show something more interesting, such as $m\angle RSW = m\angle TSU$.

1. Problem Description

Given that $m\angle RSW = m\angle TSU$ and $m\angle RST = m\angle WSU$, we need to prove that $m\angle RST = m\angle WSU$. Note that the problem statement already has the prove statement written out, so we are probably trying to show something more interesting, such as $m\angle RSW = m\angle TSU$.

2. Solution Steps

Given: $m\angle RSW = m\angle TSU$

Given: $m\angle RST = m\angle WSU$

We can write the angle $\angle RSW$ as the sum of $\angle RST$ and $\angle TSW$. Similarly, we can write $\angle TSU$ as the sum of $\angle TSW$ and $\angle WSU$. Therefore,

$m\angle RSW = m\angle RST + m\angle TSW$

$m\angle TSU = m\angle TSW + m\angle WSU$

Since $m\angle RSW = m\angle TSU$, we can write:

$m\angle RST + m\angle TSW = m\angle TSW + m\angle WSU$

Subtract $m\angle TSW$ from both sides:

$m\angle RST = m\angle WSU$

This result is actually given, so let's try to prove the original statement that $m\angle RSW = m\angle TSU$ given $m\angle RST = m\angle WSU$.

$m\angle RSW = m\angle RST + m\angle TSW$

$m\angle TSU = m\angle TSW + m\angle WSU$

Since we are given $m\angle RST = m\angle WSU$, we can substitute $m\angle RST$ for $m\angle WSU$ in the expression for $m\angle TSU$:

$m\angle TSU = m\angle TSW + m\angle RST$

So now we have

$m\angle RSW = m\angle RST + m\angle TSW$

$m\angle TSU = m\angle RST + m\angle TSW$

Since $m\angle RST + m\angle TSW = m\angle RST + m\angle TSW$, we have

$m\angle RSW = m\angle TSU$

3. Final Answer

$m\angle RSW = m\angle TSU$