find the missing angle before 3x-10 equation

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? 

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

Learn how to find the missing angle in a triangle using the angle sum property. Step-by-step solution provided with detailed calculations for each angle involved. Suitable for high school students studying geometry and triangle properties.

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