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in Circles by (36.7k points)
closed by

In the figure, ∠ABC is

A) 55° 

B) 125° 

C) 35° 

D) cant be determined

2 Answers

+1 vote
by (57.0k points)
selected by
 
Best answer

Correct option is (B) 125°

\(\because\) A, B, C & D are four points on circle.

\(\therefore\) Quadrilateral ABCD is a cyclic quadrilateral.

We know that sum of opposite angles in a cyclic quadrilateral is \(180^\circ.\)

\(\because\) \(\angle ADC\;\&\;\angle ABC\) are opposite angles in cyclic quadrilateral ABCD.

\(\therefore\) \(\angle ABC+\angle ADC\) \(=180^\circ\)

\(\Rightarrow\) \(\angle ABC\) \(=180^\circ-\angle ADC\)

\(=180^\circ-55^\circ\)    \((\because\) \(\angle ADC=55^\circ)\)

\(125^\circ\)

+1 vote
by (38.9k points)

Correct option is  B) 125°

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