Question

If arc (AB) = arc (CD) such that ∠AOB = 135°, then the measure of ∠OCD is:

• A. 35°
• B. 35°
• C. 45°
• D. 22.5°

Answer 1

The correct option is D 22.5°

Since, congruent arcs (or equal arcs) of a circle subtend equal angles at the centre.
∠AOB = ∠COD = 135°
Consider triangle DOC.
By angle sum property of a triangle, we get
∠COD + ∠OCD + ∠ODC = 180°
135° + ∠OCD + ∠ODC = 180°
∠OCD = ∠ODC (angles opposite to equal sides)
2∠OCD = 180° – 135° = 45°
∠OCD = 22.5°