Question

A quadrilateral ABCD is inscribed in a circle such that AB is a diameter and $\angle ADC={130}^{\circ }$ Find $\angle ABC$ (in degrees)

Answer 1

$\Rightarrow$ Quadrilateral $ABCD$ inscribe in a circle.

$\therefore$ Quadrilateral $ABCD$ is a cyclic quadrilateral.

$\Rightarrow$ $\angle ADC+\angle ABC={180}^o$ [ Sum of opposite angles of cyclic quadrilateral is supplementary ]

$\Rightarrow$ ${130}^o+\angle ABC={180}^o$

$\Rightarrow$ $\angle ABC={180}^o-{130}^o$

$\Rightarrow$ $\angle ABC={50}^o$