Asked by Topperlearning User | 4th Oct, 2017, 01:50: PM

Expert Answer:

begin mathsize 12px style Since comma space ABPC space is space straight a space cyclic space quadrilateral comma space opposite space pairs space of space angles space are space supplementary.
angle space straight P space plus space angle space BAC space equals space 180 degree space space space space space left parenthesis straight i right parenthesis
Similarly comma space angle space straight Q space plus space angle space ABC space equals space 180 degree space left parenthesis ii right parenthesis space space space space space space left parenthesis BCQA space is space straight a space cyclic space quadrilateral right parenthesis
angle space straight R space plus space angle space BCA space equals space 180 degree space space space space space space space space space space space space space space space space space space space left parenthesis iii right parenthesis space space space space space space left parenthesis ARBC space is space straight a space cyclic space quadrilateral right parenthesis
Adding space left parenthesis straight i right parenthesis comma space left parenthesis ii right parenthesis space and space left parenthesis iii right parenthesis
angle space straight P space plus space angle space straight Q space plus space angle space straight R space plus space angle space BAC space plus space angle space ABC space space plus angle space BCA space equals space 180 degree space plus space 180 degree space plus space 180 degree space
angle space straight P space plus space angle space straight Q space plus space angle space straight R space plus space 180 degree space equals space 540 degree space space space space space space space space space space space space space space space space space space space space left parenthesis angle space BAC space plus space angle space ABC space space plus angle space BCA space equals space 180 degree space Angles space of space straight a space triangle right parenthesis
rightwards double arrow angle space straight P space plus space angle space straight Q space plus space angle space straight R space equals space space 360 degree
Hence comma space angle space straight P space plus space angle space BAC space equals space 180 degree
angle space straight Q space plus space space angle space ABC space space equals space 180 degree
space angle space straight R space plus space angle space BCA space equals space 180 degree
and space space space angle space straight P space plus space angle space straight Q space plus space angle space straight R space space equals space 360 degree space space space space space space space space space space space space space space space space space space space space space end style

Answered by  | 4th Oct, 2017, 03:50: PM