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

Answer 1

In a cyclic quadrilateral (a quadrilateral inscribed in a circle), the opposite angles are supplementary. This means that the sum of the measures of opposite angles should equal 180 degrees.

Given that:

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

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

1. \( m\angle A + m\angle I = 180^\circ \)
2. \( m\angle E + m\angle U = 180^\circ \)

Calculating \( m\angle I \):

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

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 answer is:

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