Question

If ABCD is a cyclic quadrilateral, then which of the angles given add up to ${180}^{\circ }$?

• A. $\angle$ABC and $\angle$BCD
• B. $\angle$BAD and $\angle$ADC
• C. $\angle$BAD and $\angle$BCD
• D. $\angle$CDA and $\angle$ABD

Answer 1

The correct option is C $\angle$BAD and $\angle$BCD

Opposite angles are supplementary in a cyclic quadrilateral.
i.e., They add up to ${180}^{\circ }.$
Thus, $\angle ADC+\angle ABC={180}^{\circ }$ and $\angle BAD+\angle BCD={180}^{\circ }.$