Q.In a cyclic quadrilateral two adjacent angles are 40° and $\dfrac{\pi}{3}^{c}$. Find the angles of the quadrilateral in degree.

Step 1: Convert the given radian angle: $\frac{\pi}{3}^{c} = \frac{\pi}{3}\times\frac{180}{\pi} = 60°$. So two adjacent angles are $A=40°$ and $B=60°$.

Step 2: In a cyclic quadrilateral, opposite angles are supplementary: $A+C=180°$ and $B+D=180°$.

$C = 180°-40°=140°$, $D=180°-60°=120°$. …

Convert the radian angle to degree, then use the cyclic-quadrilateral property tha …

• Applying the supplementary rule to the two ADJACENT given angles instead of to each angle and its OPPOSITE angle. …