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

m∠I=126°
and m∠U=126°

Answer 1

To find the measures of angles \( I \) and \( U \) in the inscribed quadrilateral \( AEIU \), we can use the properties of a cyclic quadrilateral.

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, meaning:
\[
m\angle A + m\angle I = 180^\circ
\]
\[
m\angle E + m\angle U = 180^\circ
\]

Now we can calculate \( m\angle I \) and \( m\angle U \):

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

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

Thus, we have:
- \( m\angle I = 153^\circ \)
- \( m\angle U = 126^\circ \)

The correct response is:
**\( m\angle I = 153^\circ \) and \( m\angle U = 126^\circ \)**.