Question

in the given figure angle ACD= Angle ABC and CP bisects angle BCD. Prove that angle APC=angle ACP​

Answer 1

abc is equal to acp as angle that bisect each other are equal

Answer 2

begin mathsize 16px style In space the space given space figure space angle space ACD space equals space angle space ABC space space left parenthesis given right parenthesis Let space angle ACD space and space angle ABC space equals space straight x because CP space bisects space angle space BCD angle DCP space equals space angle PCB Let space angle DCP space equals space angle PCB space equals space straight y Consider space increment APC space and space increment BPC angle APC space is space external space angle space of space increment BPC therefore angle APC space equals space straight x space plus space straight y space left parenthesis external space angle space property space of space triangle right parenthesis in space increment APC comma space angle APC space equals space straight x space plus space straight y angle ACP space equals angle ACD space plus angle DCP space equals space straight x space plus space straight y space therefore angle APC space equals angle ACP  end styleure