https://file.aiquickdraw.com/mathbot/file/1727286462677sethtypv.jpg

In the diagram, we are asked to find the measure of the angle \( m \angle SVW \). 

### Observations:
1. There are two intersecting lines: line \( TU \) (vertical) and line \( SYZ \) (horizontal).
2. The angle \( SVW \) is formed at the intersection point \( V \).
3. The two angles given are:
   - \( 2x^\circ \) at \( \angle UVT \).
   - \( (3x - 5)^\circ \) at \( \angle WVT \).
   
### Step 1: Identifying relationships

Angles \( SVW \) and \( UVT \) are **vertically opposite angles**, so they are equal:
\[
m \angle SVW = 2x^\circ.
\]

### Step 2: Finding \( x \)

\( \angle SVW \) and \( \angle WVT \) are **supplementary angles** because they form a straight line. Therefore, we can use the equation:
\[
2x + (3x - 5) = 180^\circ.
\]

### Step 3: Solving for \( x \)
\[
2x + 3x - 5 = 180^\circ,
\]
\[
5x - 5 = 180^\circ,
\]
\[
5x = 185^\circ,
\]
\[
x = 37^\circ.
\]

### Step 4: Calculating \( m \angle SVW \)

Now that we know \( x = 37^\circ \), we can substitute this value into the expression for \( m \angle SVW \):
\[
m \angle SVW = 2x = 2(37^\circ) = 74^\circ.
\]

Thus, the measure of \( m \angle SVW \) is **74 degrees**.

Would you like further explanation or help with related questions? 

Here are 5 related questions to deepen your understanding:
1. How do you prove two angles are supplementary?
2. What are vertically opposite angles, and why are they always equal?
3. How do you solve linear equations involving angles in geometry?
4. Can you find the measure of \( m \angle WVT \)?
5. What other types of angles exist in parallel line and transversal scenarios?

**Tip:** Always check if angles form a linear pair or are vertically opposite, as they have clear relationships!

Learn how to calculate the measure of angle SVW using geometry theorems such as vertically opposite angles and supplementary angles. This solution involves solving a linear equation to find the value of x and applying it to angle relationships in the diagram.

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