Question

determine m∠c. enter the answer in the space provided. use numbers instead of words. m∠c = °

Explanation:

To determine \( m\angle C \), we assume the quadrilateral \( ABCD \) is cyclic (inscribed in a circle). In a cyclic quadrilateral, opposite angles are supplementary (sum to \( 180^\circ \)). If \( \angle A \) is a right angle (since there's a square or rectangle-like figure, implying \( \angle A = 90^\circ \)), then:

Step 1: Recall cyclic quadrilateral property

In a cyclic quadrilateral, \( \angle A + \angle C = 180^\circ \) (opposite angles are supplementary).

Step 2: Assume \( \angle A = 90^\circ \) (from the diagram's square/rectangle)

Substitute \( \angle A = 90^\circ \) into the supplementary angle formula:
\( 90^\circ + m\angle C = 180^\circ \)

Step 3: Solve for \( m\angle C \)

Subtract \( 90^\circ \) from both sides:
\( m\angle C = 180^\circ - 90^\circ = 90^\circ \)

Answer:

\( 90 \)