Question

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