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)

Question

Responses

m∠I=126° and m∠U=153°
m angle upper I equals 126 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=153° and m∠U=153°
m angle upper I equals 153 degrees and m angle upper U equals 153 degrees

m∠I=126° and m∠U=126°
m angle upper I equals 126 degrees and m angle upper U equals 126 degrees

Answer 1

To solve for the angles of the cyclic quadrilateral \( AEIU \) inscribed in circle \( O \), we can use the fact that the opposite angles of a cyclic quadrilateral add up to \( 180^\circ \).

Given:

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

Now, we can find \( m\angle I \) and \( m\angle U \) using the property of the cyclic quadrilateral:

1. Since \( m\angle A + m\angle I = 180^\circ \): \[ m\angle I = 180^\circ - m\angle A = 180^\circ - 27^\circ = 153^\circ \]

2. Since \( m\angle E + m\angle U = 180^\circ \): \[ m\angle U = 180^\circ - m\angle E = 180^\circ - 54^\circ = 126^\circ \]

Therefore, we find:

• \( m\angle I = 153^\circ \)
• \( m\angle U = 126^\circ \)

So the correct response is: m∠I=153° and m∠U=126°.