quadrillateral AEIU is inscribed in circle o. given M<A=27 degrees and m<E=2(m<A), find M<I and M<U.

Answer 1

First, since AEIU is inscribed in circle o, we know that the sum of the opposite angles in a quadrilateral inscribed in a circle is equal to 180 degrees. Therefore, we have:

M<A + M<I = 180
27 degrees + M<I = 180
M<I = 153 degrees

Similarly, we know that the sum of the opposite angles in a quadrilateral inscribed in a circle is equal to 180 degrees. Therefore, we have:

m<E + M<U = 180
2(M<A) + M<U = 180
2(27) + M<U = 180
54 + M<U = 180
M<U = 126 degrees

Therefore, M<I = 153 degrees and M<U = 126 degrees.