# In the given figu

Given: and

Consider ΔOAB

Here,

OBA = OAB = 20° (angles opposite to equal sides are equal)

By angle sum property

AOB + OBA + OAB = 180°

AOB + 20° + 20° = 180°

AOB = 180° – 20° – 20°

AOB = 140°

Similarly, in ΔAOC

OCA = OAC = 30° (angles opposite to equal sides are equal)

By angle sum property

AOC + OCA + OAC = 180°

AOC + 30° + 30° = 180°

AOC = 180° – 30° – 30°

AOC = 120°

Here,

CAB = OAB + OAC = 50°

Here,

2CAB = BOC (The angle subtended by an arc at the center is twice the angle subtended by the same arc on any point on the remaining part of the circle).

2CAB = BOC

2 × 50° = BOC

BOC = 100°.

BOC = 100

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