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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 ]

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

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

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

1368276_426696_ans_16dcec95bf23478093f0aa2f631fd39d.png

Mathematics

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