Question

A)
Quadrilateral
is inscribed in circle
. Given
and
, find
and
.
(1 point)
AEIU O m∠A = 27° m∠E = 2 (m∠A)
m∠I m∠U
and
m
∠
I
=
153
°
m
∠
U
=
126
°
and
m
∠
I
=
126
°
m
∠
U
=
153
°
and
m
∠
I
=
153
°
m
∠
U
=
153
°
and
m
∠
I
=
126
°
m
∠
U
=
126
°

Answer 1

AEIU is cyclic, so opposite angles are supplementary. m∠A = 27°, m∠E = 2·27° = 54°.
Thus m∠I = 180° − m∠A = 180° − 27° = 153°,
and m∠U = 180° − m∠E = 180° − 54° = 126°.