Quadrilateral AEIU is inscribed in circle O. Given m∠A=27° and m∠E=2(m∠A), find m∠I and m∠U.

Answer 1

Since quadrilateral AEIU is inscribed in circle O, opposite angles in the quadrilateral must add up to 180°. Therefore, we can find ∠I and ∠U by using the sum of angles that add up to 180°.

Given that m∠A=27° and m∠E=2(m∠A), we have m∠E = 2(27°) = 54°.

Since opposite angles in a quadrilateral inscribed in a circle are supplementary, we have:
m∠A + m∠U = 180°
27° + m∠U = 180°
m∠U = 180° - 27°
m∠U = 153°

Similarly, we have:
m∠E + m∠I = 180°
54° + m∠I = 180°
m∠I = 180° - 54°
m∠I = 126°

Therefore, m∠I = 126° and m∠U = 153°.