Certainly! Let's go step-by-step to find the missing angle and verify the process.

1. Given Angles:

   • One angle is $25^\circ$.
   • The second angle is $x + 15^\circ$.
   • The third angle is $3x - 10^\circ$.

2. Sum of Angles in a Triangle: The sum of the angles in a triangle is $180^\circ$. Therefore, we set up the equation: $25 + (x + 15) + (3x - 10) = 180$

3. Combine Like Terms: Simplify the equation by combining the constants and the $x$ terms: $25 + x + 15 + 3x - 10 = 180$ $4x + 30 = 180$

4. Solve for $x$: Subtract 30 from both sides: $4x = 150$ Divide by 4: $x = 37.5$

5. Calculate Each Angle:

   • First angle (given): $25^\circ$
   • Second angle: $x + 15 = 37.5 + 15 = 52.5^\circ$
   • Third angle: $3x - 10 = 3(37.5) - 10 = 112.5 - 10 = 102.5^\circ$

6. Verify the Sum of the Angles: $25 + 52.5 + 102.5 = 180^\circ$

Thus, the calculation confirms that the angles are correct.

To address the specific request to find the missing angle before solving the $3x - 10$ equation:

1. Calculate the other two angles given $x = 37.5$:

   • $x + 15 = 52.5^\circ$
   • $25^\circ$ (given)

2. Find the Missing Angle Directly: Subtract the known angles from 180° to find the missing angle: $180 - (25 + 52.5) = 180 - 77.5 = 102.5^\circ$

Therefore, the missing angle, which corresponds to $3x - 10$, is confirmed to be $102.5^\circ$.

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

Here are five more questions you might find interesting:

1. How do you solve a quadratic equation using the quadratic formula?
2. What are the properties of an isosceles triangle?
3. Can you explain how to find the derivative of a function?
4. How do you convert between radians and degrees?
5. What are the different methods to solve a system of linear equations?

Tip: When solving geometry problems, double-check each step to ensure the arithmetic is correct and all conditions are met.