Question

Quadrilateral AEIU is inscribed in circle O . Given m∠A=27° and m∠E=2(m∠A) , find m∠I and m∠U .(1 point) Responses m∠I=153° and m∠U=153° m angle upper I equals 153 degrees and m angle upper U equals 153 degrees m∠I=153° and m∠U=126° m angle upper I equals 153 degrees and m angle upper U equals 126 degrees m∠I=126° and m∠U=126° m angle upper I equals 126 degrees and m angle upper U equals 126 degrees m∠I=126° and m∠U=153°

Answer 1

In a cyclical quadrilateral, the opposite angles are supplementary, meaning their measures add up to 180°.

Given:

• \( m\angle A = 27° \)
• \( m\angle E = 2(m\angle A) = 2 \times 27° = 54° \)

Now, denote:

• \( m\angle I = x \)
• \( m\angle U = y \)

From the property of cyclic quadrilaterals, we have:

1. \( m\angle A + m\angle I = 180° \)
2. \( m\angle E + m\angle U = 180° \)

Using the first equation:

\[ m\angle I = 180° - m\angle A = 180° - 27° = 153° \]

Using the second equation:

\[ m\angle U = 180° - m\angle E = 180° - 54° = 126° \]

So, we have:

• \( m\angle I = 153° \)
• \( m\angle U = 126° \)

Thus, the correct response is:

m∠I=153° and m∠U=126°.