Question

Apply properties of quadrilaterals inscribed in a circle to determine the
if
and
, while the
.
(1 point)
mAD

mQU = 55°

mAU = 112°

m∠UAD = 100°
mAD =

Answer 1

m∠UAD is an inscribed angle that intercepts arc UD, so m(arc UD) = 2·m∠UAD = 2·100° = 200°.

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

Therefore mAD = 88°.