https://file.aiquickdraw.com/mathbot/file/1728496501902k4tku943.jpg

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.

Find m∠RSV given m∠RST = 114° and ∠VST = 72°.

This geometry problem involves finding m∠RSV when m∠RST is given as 114° and ∠VST is 72°. Using the concept of a linear pair, the angles on a straight line sum up to 180°. Learn how to solve it step-by-step.

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