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CBSE Class 9 Answered

Prove that the sum of either pair of opposite angles of a cyclic quadrilaterals is 180
 
Asked by Ayan | 16 Jan, 2015, 04:00: PM
answered-by-expert Expert Answer
Consider a cyclic quadrilateral PQRS inscribed in a circle with centre at O.
Join OQ and OS.
 
begin mathsize 12px style angle S P Q equals 1 half r e f l e x angle S O Q A l s o angle S R Q equals 1 half angle S O Q N o w comma space angle S P Q plus angle S R Q space equals space 1 half r e f l e x angle S O Q plus 1 half angle S O Q space equals 1 half cross times 360 to the power of 0 equals 180 to the power of 0.... left parenthesis 1 right parenthesis S i m i l l a r l y space b y space j o i n i n g space O P space a n d space O R space i t space c a n space b e space p r o v e d space t h a t angle P S R plus angle P Q R space equals 180 to the power of 0... left parenthesis 2 right parenthesis S o space e q u a t i o n space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis space s h o w s space t h a t space t h e space s u m space o f space t h e space o p p o s i t e space a n g l e s space o f space a space c y c l i c space q u a d r i l a t e r a l space i s space 180 to the power of 0. end style
Answered by Vijaykumar Wani | 16 Jan, 2015, 04:53: PM

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