Question

quadrilateral abcd is inscribed in the circle because its vertices lie on the circle, so ∠a is supplementary to ∠c. according to the inscribed quadrilateral - opposite angles theorem, the opposite angles of an inscribed quadrilateral are supplementary, meaning they add to 180°. m∠a + m∠c = 180° 81° + m∠c = 180° m∠c = 180° - 81° m∠c = 99° m∠d =

Explanation:

Step1: Apply the Inscribed Quadrilateral - Opposite Angles Theorem

The theorem states that \(m\angle B+m\angle D = 180^{\circ}\). Assume \(m\angle B = 81^{\circ}\) (if we follow the same - type relationship as for \(\angle A\) and \(\angle C\) in the given example).

Step2: Solve for \(m\angle D\)

We have the equation \(m\angle D=180^{\circ}-m\angle B\). Substitute \(m\angle B = 81^{\circ}\) into the equation: \(m\angle D = 180^{\circ}-81^{\circ}\).

Answer:

\(99\)