Consider the angles,

∠AOB and ∠ACB

Given that,

OA perpendicular AO and OB perpendicular BO

To prove: ∠AOB = ∠ACB or,

∠AOB + ∠ACB = 180^o

Proof: In a quadrilateral

∠A + ∠O + ∠B + ∠C = 360^o(Sum of angles of a quadrilateral)

180^o + ∠O + ∠C = 360^o

∠O + ∠C = 180^o

Hence, ∠AOB + ∠AOC = 180^o (i)

Also,

∠B +∠ACB = 180^o

∠ACB = 180^o – 90^o

∠ACB = 90^o (ii)

From (i) and (ii), we get

∠ACB = ∠AOB = 90^o

Hence, the angles are equal as well as supplementary.