Question
T
50º
A
170
M
H
The image shows an inscribed quadrilateral. The mAM=54°
. Determine the m∠A
.
(1 point)
m∠A=
°
50º
A
170
M
H
The image shows an inscribed quadrilateral. The mAM=54°
. Determine the m∠A
.
(1 point)
m∠A=
°
Answers
GPT-4o mini
To determine the measure of angle \( A \) in an inscribed quadrilateral, we can use the property that opposite angles of a cyclic quadrilateral are supplementary.
Given that \( m \angle AMB = 54^\circ \) and knowing that \( \angle A \) and \( \angle M \) are opposite to each other, we can find \( m \angle A \) as follows:
1. Write the relationship:
\[
m \angle A + m \angle M = 180^\circ
\]
2. Since \( m \angle AMB = 54^\circ \), then \( m \angle M = 54^\circ \).
3. Substitute into the equation:
\[
m \angle A + 54^\circ = 180^\circ
\]
4. Solve for \( m \angle A \):
\[
m \angle A = 180^\circ - 54^\circ = 126^\circ
\]
Thus, the measure of angle \( A \) is:
\[
m \angle A = 126^\circ
\]
Given that \( m \angle AMB = 54^\circ \) and knowing that \( \angle A \) and \( \angle M \) are opposite to each other, we can find \( m \angle A \) as follows:
1. Write the relationship:
\[
m \angle A + m \angle M = 180^\circ
\]
2. Since \( m \angle AMB = 54^\circ \), then \( m \angle M = 54^\circ \).
3. Substitute into the equation:
\[
m \angle A + 54^\circ = 180^\circ
\]
4. Solve for \( m \angle A \):
\[
m \angle A = 180^\circ - 54^\circ = 126^\circ
\]
Thus, the measure of angle \( A \) is:
\[
m \angle A = 126^\circ
\]