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=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=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

Given that quadrilateral AEIU is inscribed in circle O, we have the following:

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

In a cyclic quadrilateral (one inscribed in a circle), the opposite angles are supplementary. Therefore, the following relationships hold:

\[ m\angle A + m\angle I = 180^\circ \]

\[ m\angle E + m\angle U = 180^\circ \]

Now, we can calculate \( m\angle I \):

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

Next, we can calculate \( m\angle U \):

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

Thus, we have:

\[ m\angle I = 153^\circ \quad \text{and} \quad m\angle U = 126^\circ \]

The answer is:

\[ m\angle I = 153^\circ \quad \text{and} \quad m\angle U = 126^\circ \]

So the correct response is:

m∠I=153° and m∠U=126°.