Answer 1

It is given that, AB and CD are diameter with center O and `angleOBD = 50°`

We have to find `angle AOC` 

Construction: Join the point A and D to form line AD

Clearly arc AD subtends`angle ABD = 50°`  at B and `angleAOD`  at the centre.

Therefore, 

\[\angle AOD = 2\angle ABD = 100° \]         …… (1)

Since CD is a straight line then

\[\angle DOA + \angle AOC = 180° \left( \text{ Linear pair } \right)\]

`angle AOC = 180° - 100°`

             = 80°

Hence `angle AOC = 80°