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Why is the angle sum property not applicable to concave quadrilateral?(please explain elaborately and if possible with proof and example) Thank you. PS I have seen the video related to it and have still not thoroughly understood the concept.
Asked by hk.sachdev | 11 Jan, 2019, 09:00: PM
answered-by-expert Expert Answer
Concave quadrilateral has one interior angle greater than 180° as shwon in figure. In figure ABCD is a concave quadilateral.
One of the interior angle ADC is > 180°
 
Angle sum property of quadrilateral is sum of interior angles is 360°. This is valid for concave quadilateral also.
 
In figure, if we join BD, we get two triangles. we know sum of angles of triangles is 180°.
Since the cyclic quadrilateral has two triangles and all these angles are interior or part of interior angles,
sum of interior angles of cyclic quadrilateral is 360°
Answered by Thiyagarajan K | 15 Jan, 2019, 02:20: PM

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