One of the adjacent corners is 5 times smaller than the other. Find these corners.
| September 6, 2021 | education
1. Adjacent angles AOC and AOD are formed at the intersection of straight lines AB and CD.
2. AOD is 5 times less than the adjacent AHE, that is, ∠AHO = 5∠AOD.
3. The total value of adjacent angles, according to their properties, is 180 °:
AOS + AOD = 180 °. We replace in this expression ∠AOC by 5∠AOD:
5∠AOD + AOD = 180 °.
6∠AOD = 180 °.
∠AOD = 30 °.
∠AOS = 5∠AOD = 5 x 30 ° = 150 °.
Answer: ∠AOD = 30 °, ∠AOC = 150 °.
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