Answer :

Given: BC = OB and ACD = 25°


Here in Δ OBC


BOC = BCO (angles opposite to equal sides are equal)


BOC = 25°


By angle sum property


BOC + BCO + OBC = 180°


25° + 25° + OBC = 180°


50° + OBC = 180°


OBC = 180° – 50°


OBC = 130°


Here


ABC = ABO + OBC = 180°


ABO + 130° = 180°


ABO = 180° – 130°


ABO = 50°


Now, in ΔAOB


OB = OA (radius)


ABO = BAO = 50° (angles opposite to equal sides are equal)


By angle sum property


ABO + BAO + AOB = 180°


50° + 50° + AOB = 180°


AOB = 180° – (50° + 50°) = 180° – 100° = 80°


AOB = 80°


Here


DOC = AOD + AOB + BOC = 180°


AOD + 80° + 25° = 180°


AOD + 105° = 180°


AOD = 180° 105°


AOD = 75°


AOD = 75°

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