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:
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Write the relationship: \[ m \angle A + m \angle M = 180^\circ \]
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Since \( m \angle AMB = 54^\circ \), then \( m \angle M = 54^\circ \).
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Substitute into the equation: \[ m \angle A + 54^\circ = 180^\circ \]
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Solve for \( m \angle A \): \[ m \angle A = 180^\circ - 54^\circ = 126^\circ \]
Thus, the measure of angle \( A \) is: \[ m \angle A = 126^\circ \]
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