Question

In figure, $ABCD$ is a cyclic quadrilateral. Find the values of $a$ and $b$.

Answer 1

In cyclic quadrilateral

opposite angles have sum ${180}^o$

$\therefore a+7+5b+8={180}^o$

$a+5b={165}^o$ ...(1)

$2a+3+4b-3={180}^o$

$2a+4b={180}^o$ ...(2)

solve (1) and (2)

by $2\times \left(1\right)-\left(2\right)$

$6b=2\times 165-180$

$6b=330-180=150$

$b={25}^o$

$a={40}^o$