Question

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

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

mAD=115°
𝑚
𝐴
𝐷
⏜
=
115
°

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

m∠B=95.5°

Answer 1

Compute the missing arc and the inscribed angles.

Given arcs: AB = 54°, BC = 115°, CD = 86°. Then AD = 360 − (54+115+86) = 105°.

- ∠D intercepts arc AC = AB + BC = 54 + 115 = 169°, so ∠D = 169/2 = 84.5° (so "m∠D = 169°" is false; ∠D = 84.5°).
- ∠B intercepts arc ADC = AD + DC = 105 + 86 = 191°, so ∠B = 191/2 = 95.5°.

Therefore the true statement is: m∠B = 95.5°.