5. In a cyclic quadrilateral PQRS If angle P - angle R = 50 degrees. Find the measure of angle P and angle R

Asked by avantikadandapani | 17th Nov, 2014, 06:36: PM

Expert Answer:

G i v e n space t h a t space P Q R S space i s space a space c y c l i c space q u a d r i l a t e r a l. H e n c e space o p p o s i t e space a n g l e s space a r e space s u p p l e m e n t a r y. T h u s comma space angle P plus angle R equals 180 degree... left parenthesis 1 right parenthesis A l s o space g i v e n space t h a t space angle P minus angle R equals 50 degree... left parenthesis 2 right parenthesis A d d i n g space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space h a v e comma 2 angle P equals 230 degree rightwards double arrow angle P equals fraction numerator 230 degree over denominator 2 end fraction rightwards double arrow angle P equals 115 degree S u b s t i t u t i n g space t h e space v a l u e space o f space angle P space i n space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma 115 degree plus angle R equals 180 degree rightwards double arrow angle R equals 180 degree minus 115 degree rightwards double arrow angle R equals 65 degree

Answered by Vimala Ramamurthy | 18th Nov, 2014, 08:23: AM