Question

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

(1 point)
m

A
D
=
°

Answer 1

To determine \( m \angle AD \), we can use the property of angles in a cyclic quadrilateral. In a cyclic quadrilateral, the sum of the opposite angles is equal to \( 180^\circ \).

Given:
- \( m \angle QU = 55^\circ \)
- \( m \angle AU = 112^\circ \)
- \( m \angle UA = 100^\circ \)

We need to find \( m \angle AD \).

Since \( A, U, Q, D \) are points of a cyclic quadrilateral, we will look at the pairs of opposite angles:
1. \( m \angle QU + m \angle AD = 180^\circ \)
2. \( m \angle AU + m \angle UD = 180^\circ \)

From the information given:
- To calculate \( m \angle AD \), we use the first equation:

\[
m \angle AD = 180^\circ - m \angle QU
\]
\[
m \angle AD = 180^\circ - 55^\circ = 125^\circ
\]

Thus, we find that:
\[
m \angle AD = 125^\circ
\]

The final answer is:
\[
\boxed{125^\circ}
\]