Quadrilateral AEIU is inscribed in circle O. Given mLA = 27° and mLE = 2(mLA), find mLI and mLU. (1 point)

Question

OmLI = 153° and mLU = 153°
O mLI = 126° and mLU = 126°
OmLI = 153° and mLU = 126°
O mLI = 126° and mLU = 153°-

Answer 1

To solve this problem, we start by using the information provided about the cyclic quadrilateral AEIU inscribed in circle O.

1. Angles in Cyclic Quadrilaterals: The key property of a cyclic quadrilateral is that opposite angles are supplementary. Therefore, if we know one angle, we can find the opposite angle using the relationship that they add up to 180°.

2. Given Angles:

   • We have \( mLA = 27° \).
   • We are also given that \( mLE = 2(mLA) = 2(27°) = 54° \).

3. Finding mLI and mLU:

   • Since \( mLA + mLI = 180° \) (opp. angles), \[ mLI = 180° - mLA = 180° - 27° = 153°. \]
   • Since \( mLE + mLU = 180° \) (opp. angles), \[ mLU = 180° - mLE = 180° - 54° = 126°. \]

4. Conclusion:

   • Hence, we find that \( mLI = 153° \) and \( mLU = 126° \).

So, the correct answer is:

OmLI = 153° and mLU = 126°.