Question

page 6 of 6 Circles and Quadrilaterals Quick Check 2 of 52 of 5 Items 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=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=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=153° m angle upper I equals 153 degrees and m angle upper U equals 153 degrees Skip to navigation

Answer 1

To solve for the measures of angles I and U in the cyclic quadrilateral AEIU (inscribed in circle O), we can use the property that the opposite angles of a cyclic quadrilateral sum to 180°.

1. First, we are given:
- \( m∠A = 27° \)
- \( m∠E = 2(m∠A) = 2(27°) = 54° \)

2. Next, we need to find \( m∠I \) and \( m∠U \).
- Since the opposite angles of cyclic quadrilateral sum to 180°, we have:
\[
m∠A + m∠I = 180°
\]
\[
m∠E + m∠U = 180°
\]

3. Substituting the known values:
- For angle I:
\[
27° + m∠I = 180°
\]
\[
m∠I = 180° - 27° = 153°
\]

- For angle U:
\[
54° + m∠U = 180°
\]
\[
m∠U = 180° - 54° = 126°
\]

4. Therefore, we find:
- \( m∠I = 153° \)
- \( m∠U = 126° \)

The correct response is: **m∠I = 153° and m∠U = 126°**.