What is the angle if it is 37 degrees larger than the adjacent angle?
| July 29, 2021 | education
1. According to the condition of the problem, SAOB is 37 ° larger than the adjacent angle AOC.
Therefore, AOB = ∠AOC + 37 °.
2. The total value of two adjacent angles, according to their properties, is 180 °:
∠AOC + ∠AOB = 180 °.
3. We replace in this expression ∠АОВ by ∠АОС + 37 °.
AOC + AOC + 37 ° = 180 °.
2∠AOC = 180 ° – 37 ° = 143 °.
∠AOS = 143 °: 2 = 71.5 °.
∠АВ = ∠АСО + 37 ° = 71.5 ° + 37 ° = 108.5 °.
Answer: ∠AOC = 71.5 °, ∠AOB = 108.5 °.
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