Question

Apply properties of quadrilaterals inscribed in a circle to determine the mAD
𝑚
𝐴
𝐷
⏜
if mQU=55°
𝑚
𝑄
𝑈
⏜
=
55
°
and mAU=112°
𝑚
𝐴
𝑈
⏜
=
112
°
, while the m∠UAD=100°
𝑚
∠
𝑈
𝐴
𝐷
=
100
°
.

(1 point)
mAD=
𝑚
𝐴
𝐷
⏜
=
°

Answer 1

An inscribed angle measures half its intercepted arc. Angle UAD intercepts arc UD, so
m(arc UD) = 2·m∠UAD = 2·100° = 200°.

Arc UD = arc UA + arc AD, so 200° = 112° + m(arc AD). Therefore
m(arc AD) = 200° − 112° = 88°.

Answer: 88°.