https://file.aiquickdraw.com/mathbot/file/1724862324435khd1ez2p.jpg

In case you're confused the upper part of the angles says 2x+23 bottom lower part is x+13

The image shows two angles forming a right angle. The larger angle at the top is labeled as \(2x + 23^\circ\), and the smaller angle at the bottom is labeled as \(x + 13^\circ\). 

Since these two angles form a right angle (which is 90 degrees), we can write the following equation:

\[
(2x + 23) + (x + 13) = 90
\]

Let's solve this equation step by step.

### Step 1: Combine like terms

\[
2x + x + 23 + 13 = 90
\]

\[
3x + 36 = 90
\]

### Step 2: Subtract 36 from both sides

\[
3x = 90 - 36
\]

\[
3x = 54
\]

### Step 3: Divide both sides by 3

\[
x = \frac{54}{3}
\]

\[
x = 18
\]

So, \(x = 18\).

### Step 4: Find the actual angles

- The top angle: \(2x + 23 = 2(18) + 23 = 36 + 23 = 59^\circ\)
- The bottom angle: \(x + 13 = 18 + 13 = 31^\circ\)

Thus, the angles are \(59^\circ\) and \(31^\circ\), which sum up to \(90^\circ\), confirming that the solution is correct.

Would you like more details or have any questions about this solution? 

Here are some related questions you might find interesting:

1. What if the two angles did not form a right angle? How would the equation change?
2. How do you determine the angles if only one angle is given?
3. Can you create a general formula for the angles in terms of \(x\)?
4. What if the top angle were \(3x + 10\) and the bottom angle were \(x + 20\)? How would you solve it?
5. How can this problem be extended to find the angles in a triangle?

**Tip:** Remember that the sum of angles in any right-angled triangle adds up to 90 degrees for the two non-right angles.

Explore how to solve angles in a right triangle where the larger angle is represented as 2x+23 degrees and the smaller angle as x+13 degrees. Follow a step-by-step solution with detailed equations and calculations. Suitable for students in Grades 7-9 studying geometry and angle relationships.

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