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The problem shows a geometric diagram with angles marked at point \( W \). The given angles are:

- \( 40^\circ \) (angle \( ZWY \)),
- \( 2x + 10 \) (angle \( YWX \)).

The angle at \( W \) forms a right angle (indicated by the small square), which is equal to \( 90^\circ \).

To find \( x \), we use the fact that the sum of the angles around point \( W \) must equal \( 90^\circ \). Therefore, we can set up the equation:

\[
(2x + 10) + 40 = 90
\]

Simplifying this equation:

\[
2x + 10 + 40 = 90
\]

\[
2x + 50 = 90
\]

\[
2x = 90 - 50
\]

\[
2x = 40
\]

\[
x = \frac{40}{2} = 20
\]

Thus, the value of \( x \) is \( 20 \).

Would you like further details or have any other questions?

Here are 5 related questions to expand on this concept:
1. How would the equation change if the angle \( ZWY \) was \( 50^\circ \)?
2. How do you verify that the sum of angles in a right-angled triangle always equals \( 90^\circ \)?
3. What if the equation was \( 3x + 10 \) instead of \( 2x + 10 \)? How would you solve for \( x \)?
4. How do you use the properties of complementary angles to solve problems like this?
5. Can the same method be applied if the sum of angles was less than or greater than \( 90^\circ \)?

**Tip**: Always check for complementary angles when dealing with right-angle problems; they must sum to \( 90^\circ \).

Find the value of x given a right angle at point W, with angles (2x + 10) and 40 degrees.

Learn how to solve a right-angle geometry problem where the angles (2x + 10) and 40 degrees sum up to 90°. This step-by-step explanation includes key algebraic and geometric concepts, suitable for students in Grades 6-8.

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