Answer: The correct option is (C) 84.
Step-by-step explanation: We are to find the value of c from the figure shown.
We see from the figure that
a quadrilateral is inscribed in a circle with opposite pairs of angles with measurements (c° and 96°) and (d° and 100°). So, the given quadrilateral is a cyclic one.
We know that
the sum of the measurements of the opposite angles of a cyclic quadrilateral is 180°.
Therefore, we must have
[tex]c^\circ+96^\circ=180^\circ\\\\\Rightarrow c^\circ=180^\circ-96^\circ\\\\\Rightarrow c^\circ=84^\circ\\\\\Rightarrow c=84.[/tex]
Thus, the required value of c is 84.
Option (C) is CORRECT.
