Question

BOD=140°
Find DCP
O is centre of the circle

Answer 1

Easy!


Angle BAD = 1/2 angle BOD

(the angle subtended by a chord on the centre, is double of the angle subtended by it on the point on circumference)

angle bad = 1/2 × 140

angle bad = 70°


Now ABCD is cyclic quadrilateral. So opposite angle would be supplementary


So angle bad + angle BCD = 180

angle BCD = 180 - angle bad

angle BCD = 180 - 70

angle BCD = 110°

now DCP and BCD are linear pair

so angle DCP = 180 - 110

angle DCP = 70°

Answer is 70°