In the image, we are given:

• $m \angle RST = 114^\circ$
• $\angle VST = 72^\circ$

We are asked to find $m \angle RSV$.

Solution:

The key here is to realize that angles on a straight line add up to $180^\circ$. Thus, $\angle RST$ and $\angle RSV$ form a linear pair, meaning:

$m \angle RST + m \angle RSV = 180^\circ$

Substituting $m \angle RST = 114^\circ$:

$114^\circ + m \angle RSV = 180^\circ$

Now, solving for $m \angle RSV$:

$m \angle RSV = 180^\circ - 114^\circ = 66^\circ$

Thus, $m \angle RSV = 66^\circ$.

Would you like further details on this, or do you have any questions?

Here are 5 related questions to expand on this concept:

1. How do we know that $m \angle RSV$ and $m \angle RST$ form a linear pair?
2. What other methods could be used to verify the angle $m \angle RSV$?
3. If $m \angle VST$ changed to 80°, how would that affect $m \angle RSV$?
4. Can you explain the concept of supplementary angles in more detail?
5. What happens to $m \angle RSV$ if $m \angle RST$ becomes obtuse?

Tip: Remember that angles on a straight line always sum to $180^\circ$, which is a key concept in solving many geometry problems.