U

Question

OK
A
D
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=
°

Answer 1

To solve for \( mAD \), we'll use the properties of a cyclic quadrilateral. In a cyclic quadrilateral, the opposite angles sum up to 180 degrees.

Given the angles:

• \( mQU = 55^\circ \)
• \( mAU = 112^\circ \)
• \( m\angle UAD = 100^\circ \)

Let's label the points based on the angles:

• \( mQU \) and \( mAD \) are opposite angles in the cyclic quadrilateral.
• Thus, \( mQU + mAD = 180^\circ \).

First, we can find \( mAD \): \[ mAD = 180^\circ - mQU \] \[ mAD = 180^\circ - 55^\circ = 125^\circ \]

Now we have \( mAD = 125^\circ \).

So, the answer is: \[ mAD = 125^\circ \]