Postulate (Select all that apply.) \( \square \mathrm{m} \angle \mathrm{BOF}+\mathrm{m} \angle \mathrm{GOF}=\mathrm{m} \angle \mathrm{BOG} \) \( \square \mathrm{m} \angle \mathrm{AOB}+\mathrm{m} \angle \mathrm{BOC}=\mathrm{m} \angle \mathrm{AOC} \) \( \square \mathrm{m} \angle \mathrm{COD}+\mathrm{m} \angle \mathrm{FOD}=\mathrm{m} \angle \mathrm{FOC} \) \( \square \mathrm{m} \angle \mathrm{BOD}+\mathrm{m} \angle \mathrm{FOG}=\mathrm{m} \angle \mathrm{BOF} \) \( \square \mathrm{m} \angle \mathrm{EOF}+\mathrm{m} \angle \mathrm{FOA}=\mathrm{m} \angle \mathrm{AOE} \) \( \square \mathrm{m} \angle \mathrm{BOD}+\mathrm{m} \angle C O E=\mathrm{m} \angle B O E \)

To determine which postulates apply, we need to analyze the statements provided. Each statement represents a relationship between angles, specifically that the sum of two angles equals a third angle. This is a fundamental property of angles in geometry, often referred to as the Angle Addition Postulate. Let's evaluate each statement: 1. **\( \mathrm{m} \angle \mathrm{BOF} + \mathrm{m} \angle \mathrm{GOF} = \mathrm{m} \angle \mathrm{BOG} \)** This statement suggests that the sum of angles \( \angle BOF \) and \( \angle GOF \) equals angle \( \angle BOG \). This is a valid application of the Angle Addition Postulate. 2. **\( \mathrm{m} \angle \mathrm{AOB} + \mathrm{m} \angle \mathrm{BOC} = \mathrm{m} \angle \mathrm{AOC} \)** This statement indicates that the sum of angles \( \angle AOB \) and \( \angle BOC \) equals angle \( \angle AOC \). This is also a valid application of the Angle Addition Postulate. 3. **\( \mathrm{m} \angle \mathrm{COD} + \mathrm{m} \angle \mathrm{FOD} = \mathrm{m} \angle \mathrm{FOC} \)** This statement suggests that the sum of angles \( \angle COD \) and \( \angle FOD \) equals angle \( \angle FOC \). This is a valid application of the Angle Addition Postulate. 4. **\( \mathrm{m} \angle \mathrm{BOD} + \mathrm{m} \angle \mathrm{FOG} = \mathrm{m} \angle \mathrm{BOF} \)** This statement indicates that the sum of angles \( \angle BOD \) and \( \angle FOG \) equals angle \( \angle BOF \). This is a valid application of the Angle Addition Postulate. 5. **\( \mathrm{m} \angle \mathrm{EOF} + \mathrm{m} \angle \mathrm{FOA} = \mathrm{m} \angle \mathrm{AOE} \)** This statement suggests that the sum of angles \( \angle EOF \) and \( \angle FOA \) equals angle \( \angle AOE \). This is a valid application of the Angle Addition Postulate. 6. **\( \mathrm{m} \angle \mathrm{BOD} + \mathrm{m} \angle C O E = \mathrm{m} \angle B O E \)** This statement indicates that the sum of angles \( \angle BOD \) and \( \angle COE \) equals angle \( \angle BOE \). This is a valid application of the Angle Addition Postulate. ### Conclusion: All the statements provided are valid applications of the Angle Addition Postulate. Therefore, the correct selections are: - \( \square \mathrm{m} \angle \mathrm{BOF} + \mathrm{m} \angle \mathrm{GOF} = \mathrm{m} \angle \mathrm{BOG} \) - \( \square \mathrm{m} \angle \mathrm{AOB} + \mathrm{m} \angle \mathrm{BOC} = \mathrm{m} \angle \mathrm{AOC} \) - \( \square \mathrm{m} \angle \mathrm{COD} + \mathrm{m} \angle \mathrm{FOD} = \mathrm{m} \angle \mathrm{FOC} \) - \( \square \mathrm{m} \angle \mathrm{BOD} + \mathrm{m} \angle \mathrm{FOG} = \mathrm{m} \angle \mathrm{BOF} \) - \( \square \mathrm{m} \angle \mathrm{EOF} + \mathrm{m} \angle \mathrm{FOA} = \mathrm{m} \angle \mathrm{AOE} \) - \( \square \mathrm{m} \angle \mathrm{BOD} + \mathrm{m} \angle C O E = \mathrm{m} \angle B O E \)