In the figure, given below, AD = BC, ∠ BAC=30∘ and ∠CBD=70∘. Find: ∠ ABC
In the figure, ABCD is a cyclic quadrilateral AC and BD are its diagonals ∠ BAC=30∘ and ∠ CBD=70∘
∠ CAD=∠ CBD=70∘
Similarly ∠ BAC=∠ BDC=30∘
∵ AD = BC (given)
∴ ∠ ABCD is an isosceles trapezium
and AB || DC
∠ BAC=∠ DCA (alternate angle)
⇒ DCA=30∘
∴ ABD=∠DAC=30∘
(Angles in the same segment)
∠ ABC=∠ ABD+∠ CBD=30∘+70∘=100∘