Find the AOB angle adjacent to the BOC angle if the AOB angle is 43 (deg) less than the BOC angle.
| May 26, 2021 | education
1. АВ is less than the adjacent ∠ВОС by 43 ° according to the condition of the problem, that is ∠ВОС = ∠АОВ + 43 °.
2. The total value of adjacent angles, according to their properties, is 180 °:
∠AOВ + ∠ВOС = 180 °. We replace in this expression ∠ВОС by ∠АОВ + 43 °:
∠АОВ + ∠АОВ + 43 ° = 180 °.
2∠АВ = 180 ° – 43 ° = 137 °.
∠АВ = 137 °: 2 = 68.5 °.
Answer: AOB is equal to 68.5 °.
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