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To solve the problem, we start by understanding that angles \( \angle U \) and \( \angle V \) are supplementary. This means their measures add up to \( 180^\circ \).

Given:
\[
m\angle U = 3x^\circ, \quad m\angle V = 2(m\angle U)
\]

Substitute the expression for \( m\angle U \) into the formula for \( m\angle V \):

\[
m\angle V = 2(3x) = 6x^\circ
\]

Since \( \angle U \) and \( \angle V \) are supplementary, we have:

\[
m\angle U + m\angle V = 180^\circ
\]

Substitute the values for \( m\angle U \) and \( m\angle V \):

\[
3x + 6x = 180
\]

Combine like terms:

\[
9x = 180
\]

Solve for \( x \):

\[
x = \frac{180}{9} = 20
\]

So, the value of \( x \) that makes \( \angle U \) and \( \angle V \) supplementary is:

\[
\boxed{x = 20}
\]

Would you like more details or have any other questions?

Here are some related questions:
1. What are supplementary angles?
2. How do we determine if two angles are supplementary or complementary?
3. Can two right angles be supplementary?
4. How to solve for unknown angles using algebra?
5. What are complementary angles, and how do they differ from supplementary angles?

**Tip:** When dealing with angle relationships, always remember that supplementary angles add up to 180 degrees, while complementary angles add up to 90 degrees.

Find the value of x that makes ∠U and ∠V supplementary, given m∠U = 3x° and m∠V = 2(m∠U).

Learn how to solve for x when given the angle measures m∠U = 3x° and m∠V = 2(m∠U), ensuring the angles are supplementary. Step-by-step solution provided. Suitable for Grades 7-9.

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