Question

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






mAD
=
115

Answer 1

Interpret the given arcs around the circle in order A–B–C–D:

m(AB) = 54°, m(BC) = 115°, m(CD) = 86°.
So m(AD) = 360 − (54+115+86) = 105°.

An inscribed angle equals half the measure of its intercepted arc. Therefore:

- m∠B = 1/2 (arc AD + arc DC) = 1/2 (105 + 86) = 95.5°
- m∠D = 1/2 (arc AB + arc BC) = 1/2 (54 + 115) = 84.5°
- m∠A = 1/2 (arc BC) = 1/2 (115) = 57.5°

So the true statement from the choices is: m∠B = 95.5°. (m∠D = 169° and mAD = 115° are false.)