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

m∠E = 2·27° = 54°. In a cyclic quadrilateral opposite angles are supplementary, so

m∠I = 180° − m∠A = 180° − 27° = 153°
m∠U = 180° − m∠E = 180° − 54° = 126°.

Answer: m∠I = 153°, m∠U = 126°.