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The problem states that \(\angle UVW\) and \(\angle XYZ\) are complementary angles, which means their measures add up to 90°.

You are given:
- \( m\angle UVW = (x - 10)^\circ \)
- \( m\angle XYZ = (4x - 10)^\circ \)

Since the angles are complementary, we can write the equation:

\[
(x - 10) + (4x - 10) = 90
\]

Let's solve for \(x\):

\[
x - 10 + 4x - 10 = 90
\]
\[
5x - 20 = 90
\]
\[
5x = 110
\]
\[
x = 22
\]

Now that we have \(x\), we can find the measures of the angles:

1. \( m\angle UVW = x - 10 = 22 - 10 = 12^\circ \)
2. \( m\angle XYZ = 4x - 10 = 4(22) - 10 = 88 - 10 = 78^\circ \)

Thus:
- \( m\angle UVW = 12^\circ \)
- \( m\angle XYZ = 78^\circ \)

Would you like any more details or clarifications? Here are five related questions to extend your understanding:

1. What is the definition of supplementary angles?
2. How do we verify if two angles are complementary using their algebraic expressions?
3. Can complementary angles be obtuse?
4. How would the equation change if the angles were supplementary instead?
5. How would the problem change if one of the angles were expressed as \(3x - 20^\circ\)?

**Tip:** Always check if the sum of complementary angles equals 90° after solving for \(x\).

Find the measure of each angle: ∠UVW and ∠XYZ are complementary angles, m∠UVW = (x - 10)°, and m∠XYZ = (4x - 10)°.

Solve the problem of finding the measures of two complementary angles, UVW and XYZ, where m∠UVW = (x - 10)° and m∠XYZ = (4x - 10)°. Follow a step-by-step solution using algebra to determine x and calculate the angles.

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