Find the adjacent angles that are obtained at the intersection of two straight lines if their degree
| May 3, 2021 | education
Find the adjacent angles that are obtained at the intersection of two straight lines if their degree measures are in the ratio of 3: 7.
1. Adjacent angles АОС and АОD are formed at the intersection of straight lines AB and CD. ∠AOD / ∠AOC = 3/7.
2. ∠АD / ∠АОС = 3/7 according to the problem statement. ∠AOD = 3∠AOC / 7.
3. The total value of two adjacent angles, according to their properties, is 180 °:
∠АС + АОD = 180 °. We replace AOD with 3∠AOC / 7.
∠AOC + 3∠AOC / 7 = 180 °.
10 ° AOC = 7 x 180 °.
∠AOC = 126 °.
∠AOD = 3∠AOC / 7 = 3 x 126/7 = 54 °.
Answer: AOC = 126 °, ∠AOD = 54 °.
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