Question

∠АОВ-∠АОС=27°, ∠АОВ-∠ВОС=42°. Найти ∠АОВ

Answer 1

угол АОВ- угол АОС=угол ВОС=27°

угол АОВ - угол ВОС=угол АОС=42°

угол АОВ= угол АОС+ угол ВОС=42+27=69⁰

Answer 2

We can start by using the first equation to express ∠АОС in terms of ∠АОВ:

∠АОВ - ∠АОС = 27°

∠АОС = ∠АОВ - 27°

Then we can substitute this expression for ∠АОС in the second equation:

∠АОВ - ∠ВОС = 42°

∠АОВ - (∠АОС + ∠ВОС) = 42°

∠АОВ - (∠АОВ - 27° + ∠ВОС) = 42°

Simplifying:

27° + ∠ВОС = 42°

∠ВОС = 15°

Now we can use the first equation again to solve for ∠АОВ:

∠АОВ - ∠АОС = 27°

∠АОВ - (∠АОВ - 27°) = 27°

27° = 27°

Therefore, we have not obtained any new information about ∠АОВ from this equation. However, we can use the fact that ∠ВОС = 15° to find the value of ∠АОВ in another way.

Since the sum of the angles in triangle AOV is 180°, we have:

∠АОВ + ∠АОС + ∠ВОС = 180°

Substituting ∠АОС = ∠АОВ - 27° and ∠ВОС = 15°:

∠АОВ + (∠АОВ - 27°) + 15° = 180°

2∠АОВ - 12° = 180°

2∠АОВ = 192°

∠АОВ = 96°

Therefore, the value of ∠АОВ is 96°.