mAD= 233°
This can be determined by applying the property that the opposite angles of a quadrilateral inscribed in a circle are supplementary. So, we have:
mQU + mAD = 180°
55° + mAD = 180°
mAD = 180° - 55°
mAD = 125°
Then, the sum of the angles in triangle UAD is 180°.
mAU + mUAD + mAD = 180°
112° + 100° + mAD = 180°
212° + mAD = 180°
mAD = 180° - 212°
mAD = -32°
Since angle AD is an exterior angle of triangle QAD, we can determine the measure as:
mAD = mQ + mAU
mQ = mAD - mAU
mQ = 125° - 112°
mQ = 13°
Finally, we find:
mAD = mQ + mAU
mAD = 13° + 112°
mAD = 125°
Therefore, mAD = 233°.
Quadrilateral upper Q upper U upper A upper D is drawn within a circle such that all vertices touch the edge of the circle.
Apply properties of quadrilaterals inscribed in a circle to determine the mAD
if mQU=55°
and mAU=112°
, while the m∠UAD=100°
.
(1 point)
mAD=
°
1 answer
1 answer