Q. 185.0( 1 Vote )

# In the given figu

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,

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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