If O is the centre of a circle, ABCD is cyclic Arc BCD subtends an angle of 140 degrees - Maths - Circles

Question

If O is the centre of a circle, ABCD is cyclic Arc BCD subtends an
angle of 140 degrees at the centre , BC is produced to P and CD is
joined Find the measure of angle DCP

Anuradha Sharma · Accepted Answer

∠BOD=140 degreeSO ∠BRD=70 degreebecause angle made by an arc on center is double as that of made onthe circumfrence in the same segment
So now ∠BRD=70 and BCDR is a cyclic quadrilateral so, ∠BRD+∠BCD=18070+∠BCD=180∠BCD=110Now ∠BCD and ∠DCP are linear pair so, ∠BCD+∠DCP=180∠DCP=70 degree

If O is the centre of a circle, ABCD is cyclic. Arc BCD subtends an angle of 140 degrees at the centre , BC is produced to P and CD is joined. Find the measure of angle DCP.