Find the value of $a$ if ABCD is a cyclic quadrilateral if $\angle 1:\angle 2=3:6$

Concept: Every angle of a cyclic quadrilateral is on a circle (circumscribed circle), and the sum of any two opposite angles of a cyclic quadrilateral is ${180}^{°}$

Here, ABCD is a cyclic quadrilateral.

Then, sum of any pair of opposite angles of cyclic quadrilateral is ${180}^{°}$

$\Rightarrow \angle 1+\angle 2={180}^{°}$

$\begin{array}{l}\Rightarrow 3k+6k={180}^{°}\\ \Rightarrow k={20}^{°}\end{array}$

Exterior angle formed when one side of cyclic quadrilateral is produced is equal to the interior opposite angle.

Then, $a=\angle 1$

$\begin{array}{l}\Rightarrow a=3k\\ \Rightarrow a={60}^{°}\end{array}$

Hence, $a={60}^{°}$