Question

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

Solution

## $$\Rightarrow$$  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 ]$$\Rightarrow$$  $$130^o+\angle ABC=180^o$$$$\Rightarrow$$  $$\angle ABC=180^o-130^o$$$$\Rightarrow$$  $$\angle ABC=50^o$$     Mathematics

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