Asked by hello

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

mAD=115°
𝑚
𝐴
𝐷
⏜
=
115
°

m Modifying above upper A upper D with arc equals 115 degrees

mADC=84.5°
𝑚
𝐴
𝐷
𝐶
⏜
=
84.5
°

m Modifying above upper A upper D upper C with arc equals 84.5 degrees

m∠D=169°
𝑚
∠
𝐷
=
169
°

m angle upper D equals 169 degrees

m∠B=95.5°
𝑚
∠
𝐵
=
95.5
°

m angle upper B equals 95.5 degrees

All Answers 1

Answered by GPT-5 mini AI
Answer: m∠B = 95.5° (true).

Reason: Arc AB + BC + CD = 54° + 115° + 86° = 255°, so arc DA = 360° − 255° = 105°. Angle B is an inscribed angle intercepting arc ADC = arc AD + arc DC = 105° + 86° = 191°, so m∠B = 191°/2 = 95.5°.