Consider the angles,
∠AOB and ∠ACB
Given that,
OA perpendicular AO and OB perpendicular BO
To prove:
∠AOB = ∠ACB or,
∠AOB + ∠ACB = 180°
Proof: In a quadrilateral
∠A + ∠O + ∠B + ∠C = 360°(Sum of angles of a quadrilateral)
180° + ∠O + ∠C = 360°
∠O + ∠C = 180°
Hence,
∠AOB + ∠AOC = 180°(i)
Also,
∠B +∠ACB = 180°
∠ACB = 180° – 90°
∠ACB = 90°(ii)
From (i) and (ii), we get
∠ACB = ∠AOB = 90°
Hence, the angles are equal as well as supplementary