A, B, C and D are points on the circumference of a circle, centre O: Angle BAD = 112° and angle DCO = 33° - OCR - GCSE Maths - Question 17 - 2019 - Paper 5

To find angle y, we can use the properties of angles in a circle.

1. Angle CDB: In triangle CDB, angle CDB is an external angle. According to the external angle theorem, an external angle is equal to the sum of the two opposite internal angles. Therefore: $\text{Angle CDB} = \text{Angle BAD} + \text{Angle DCO} = 112° + 33° = 145°\n$

2. Angle y: Angle y is the angle formed at point A (the angle subtended by arc BC at the circumference). According to the inscribed angle theorem: $\text{Angle y} = \frac{1}{2} \times \text{Angle CDB} = \frac{1}{2} \times 145° = 72.5°.$

However, as CDB is externally positioned, angle BAD is complementary to angle ODC, hence we have: $\text{Angle y} = 180° - \text{Angle DCO} - \text{Angle DAB} = 180° - 33° - 112° = 35°.$

Thus, angle y is confirmed to be 35°.