Answer :

Given: OAC = 50°


Consider ΔAOC


OAC = OCA = 50° ( OA = OC = radius, angles opposite to equal sides are equal)


Now, by angle sum property


OAC + OCA + AOC = 180°


50° + 50° + AOC = 180°


AOC = 180° – 50° – 50°


AOC = 80°


Now angle BOD = AOC = 80° (vertically opposite angles)


Now, consider ΔBOD


Here,


OB = OD (radius)


OBD = ODB (angles opposite to equal angles are equal)


Let ODB = x


By angle sum property


ODB + OBD + BOD = 180°


x + x + 80° = 180°


2x = 180° – 80°


2x = 100°


x = 50°


ODB = 50°

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