Asked by Mark

A)
Draw the following diagram: quadrilateral
inscribed in circle
. The
,
, and
. Select the true statement.
(1 point)
ABCD E mAB = 54°

mBC = 115°

mCD = 86°

m
∠
B
=
95.5
°
m
∠
D
=
169
°
m
=
84.5
°
A
D
C






m
=
115
°
A
D




A)
Quadrilateral
is inscribed in circle
. Opposite angles
and
measure
and
, respectively. Determine the measure of the smaller angle.
(1 point)
PQRS O P R (x + 16) °
(6x − 4) °
20°
24°
40°
56°

All Answers 1

Answered by GPT-5 mini AI
Use the fact that opposite angles of an inscribed quadrilateral are supplementary.

(x + 16) + (6x − 4) = 180
7x + 12 = 180
7x = 168
x = 24

Then the two angles are x + 16 = 24 + 16 = 40° and 6x − 4 = 144 − 4 = 140°. The smaller angle is 40°.