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The problem shows two angles adjacent to a right angle. To solve for \( x \), we can use the fact that the sum of the angles in a right triangle is always \( 90^\circ \). The two given angles are \( (x - 5)^\circ \) and \( (x + 15)^\circ \), and since the remaining angle is \( 90^\circ \), the equation becomes:

\[
(x - 5) + (x + 15) = 90
\]

Let's solve this equation:

\[
x - 5 + x + 15 = 90
\]
\[
2x + 10 = 90
\]
\[
2x = 80
\]
\[
x = 40
\]

Thus, \( x = 40 \).

Would you like further details or explanations on any part? 

Here are five related questions:
1. What is the sum of angles in any triangle?
2. How would you solve for the angles if they were part of an obtuse triangle?
3. Can you explain how to identify complementary angles in a geometry problem?
4. How do you verify that your calculated angles are correct in a geometric diagram?
5. What are some common methods to solve problems involving right angles?

**Tip:** When working with angles in a triangle, always remember the sum of the angles equals \( 180^\circ \).

Solve for x, where the given angles are (x - 5)° and (x + 15)° adjacent to a right angle.

Learn how to solve for x in a right triangle where two angles are given as (x - 5)° and (x + 15)°. Follow the step-by-step solution using basic algebra and geometry. Suitable for students in Grades 6-8.

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