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The problem asks to find the value of \( x \) given that the angle \( \angle VUX = 10x + 8^\circ \) and the diagram shows that the angle \( \angle WUX = 90^\circ \), with an angle \( \angle VUW = 48^\circ \).

Since the angles \( \angle VUX \) and \( \angle VUW \) form a part of a right angle (\( 90^\circ \)) at point \( U \), we can set up an equation to solve for \( x \).

Here are the steps:

1. The two angles, \( \angle VUX \) and \( \angle VUW \), must sum up to \( 90^\circ \), because they are part of a right angle at point \( U \):
   \[
   \angle VUX + \angle VUW = 90^\circ
   \]
2. Substitute the known values:
   \[
   (10x + 8^\circ) + 48^\circ = 90^\circ
   \]
3. Simplify the equation:
   \[
   10x + 8 + 48 = 90
   \]
   \[
   10x + 56 = 90
   \]
4. Subtract 56 from both sides:
   \[
   10x = 90 - 56
   \]
   \[
   10x = 34
   \]
5. Divide both sides by 10:
   \[
   x = \frac{34}{10} = 3.4
   \]

Thus, the value of \( x \) is \( 3.4 \).

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. What would the value of \( x \) be if the angle \( \angle VUX \) was \( 12x + 6^\circ \)?
2. How do you calculate the sum of interior angles in different types of triangles?
3. If \( \angle VUX \) was an obtuse angle, how would that affect the equation setup?
4. Can two angles sum up to more than \( 180^\circ \) in a triangle? Why or why not?
5. How do you define complementary and supplementary angles?

**Tip:** Always check the types of angles involved in a problem (like complementary or supplementary) to set up correct equations for unknowns.

If angle VUX is 10x + 8, find the value of x.

Learn how to find the value of x when given that angle VUX is 10x + 8 and the angles are complementary. Understand key concepts in algebra and geometry, including solving linear equations and applying the Complementary Angles Theorem. Suitable for students in Grades 7-9.

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