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

When we dive into angles, we're stepping into the world of geometry where the relationships between angles define so much of what we see. The postulates you’ve listed resemble the fundamental properties related to angle addition. Essentially, if two angles share a common ray, you can fold them together to find the total measure, just like how you can combine two pieces of chocolate to make a larger piece! In real-world scenarios, understanding angles is crucial in fields such as architecture and engineering. For instance, when designing a roof, engineers must calculate the angles of the beams to ensure that everything fits together perfectly and is structurally sound. It's like constructing a puzzle where every angle needs to be precise to hold up the entire structure!