Given that \( \triangle XYZ \) is a triangle and the angles are labeled as follows:
- \( \angle XWZ = 90^\circ \)
- \( \angle XWY = 5x + 5 \)
- \( \angle YWZ = 2x + 8 \)

In any triangle, the sum of the angles is always \( 180^\circ \). Therefore, we can set up the following equation:

\[
\angle XWZ + \angle XWY + \angle YWZ = 180^\circ
\]

Substituting the given values:

\[
90 + (5x + 5) + (2x + 8) = 180
\]

Now, let's solve for \( x \).

1. Combine like terms:

\[
90 + 5x + 5 + 2x + 8 = 180
\]

\[
7x + 103 = 180
\]

2. Subtract 103 from both sides:

\[
7x = 77
\]

3. Divide both sides by 7:

\[
x = 11
\]

Thus, \( x = 11 \).

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the measure of \( \angle XWY \) when \( x = 11 \)?
2. How would the triangle change if \( \angle XWZ \) was not a right angle?
3. What if one of the angles was expressed as \( 3x + 2 \)? How would the solution change?
4. Can you find the length of the sides using trigonometry if the sides were given?
5. How does the sum of angles relate to non-Euclidean geometry?

**Tip:** Always check if the sum of angles in a triangle equals 180° to verify your calculations.

Explore how to find the value of x in a triangle with angles XWZ = 90°, XWY = 5x + 5, and YWZ = 2x + 8 using the angle sum property of triangles. Detailed step-by-step solution provided.

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