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

Answer 1

To solve for the angles \( m\angle I \) and \( m\angle U \) in the cyclic quadrilateral AEIU inscribed in circle O, we can use the properties of inscribed angles.

Given:

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

In a cyclic quadrilateral, the opposite angles are supplementary, which means that: \[ m\angle A + m\angle I = 180^\circ \] \[ m\angle E + m\angle U = 180^\circ \]

Now we can substitute the values we know into these equations:

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

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

Thus, we find:

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

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