https://file.aiquickdraw.com/mathbot/file/1728522863323dsg0iotd.jpg

The image shows a right triangle with three angles. The given angles are:

- A right angle (90°)
- One angle labeled as \(48^\circ\)
- Another angle labeled as \((3x - 15)^\circ\)

Since the sum of all angles in a triangle is always \(180^\circ\), we can use this information to solve for \(x\).

### Step-by-step solution:
1. The sum of the angles in the triangle is:
   \[
   90^\circ + 48^\circ + (3x - 15)^\circ = 180^\circ
   \]

2. Combine the known angles:
   \[
   90^\circ + 48^\circ = 138^\circ
   \]

3. Substitute this into the equation:
   \[
   138^\circ + (3x - 15)^\circ = 180^\circ
   \]

4. Simplify the equation:
   \[
   3x - 15 = 180^\circ - 138^\circ
   \]
   \[
   3x - 15 = 42^\circ
   \]

5. Solve for \(3x\):
   \[
   3x = 42^\circ + 15^\circ
   \]
   \[
   3x = 57^\circ
   \]

6. Solve for \(x\):
   \[
   x = \frac{57^\circ}{3} = 19^\circ
   \]

Thus, the correct value of \(x\) is **19**, not 60 as shown in your attempt.

Would you like more details or have any questions?

### Related questions:
1. What is the sum of the angles in any triangle?
2. How do we calculate unknown angles in a triangle when two angles are given?
3. What are the properties of a right triangle?
4. Can the value of \(x\) affect other properties of this triangle (e.g., side lengths)?
5. How would you solve this problem if the triangle wasn’t a right triangle?

**Tip:** In any triangle, always remember that the sum of the angles is 180°.

The measures of the angles of a triangle are shown in the figure below. Solve for x.

In this geometry problem, solve for x in a triangle where the angles are given as (3x-15)°, 48°, and 90°. Learn how to apply the triangle sum theorem and algebraic equations to find the value of x.

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