Answer to Question #145383 in Geometry for Peace

Question #145383
In the following fiNine students are seated evenly around a circular table. They are
marked on the circumference of the circle as A, B, C, D, E, F, G, H, I.
If the center of the circle is situated at point O, what is m<OAD
1
Expert's answer
2020-11-22T13:25:22-0500

Since, they are seated evenlyaround a circular table,Distance betweenA,B,C,D,...,I  is360°9=40°m<AOD=40°×3=120°m<AOD+m<OAD+m<ODA=180°m<ODA=m<OAD120°+2m<OAD=180°2m<OAD=60°m<OAD=30°\displaystyle\textsf{Since, they are seated evenly}\\ \textsf{around a circular table,}\\ \textsf{Distance between}\, A, B, C, D,...,I \,\, \textsf{is}\\ \frac{360\degree}{9} = 40\degree\\ m<AOD = 40\degree \times 3 = 120\degree\\ m<AOD + m<OAD + m<ODA = 180\degree\\ m<ODA = m<OAD\\ 120\degree + 2m<OAD = 180\degree\\ 2m<OAD = 60\degree\\ m<OAD = 30\degree


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