𝐴, 𝐵, 𝐶 and 𝐷 are points on a circle.𝑃𝐴 is a tangent to the circle.Angle 𝑃𝐴𝐷=39∘Angle 𝐵𝐶𝐷=103∘Calculate the size of angle 𝐴𝐷𝐵.(5 marks)

Step 1: Identify the known angles. We know that 𝑃𝐴𝐷 = 39° and 𝐵𝐶𝐷 = 103°.

Step 2: Use the property of a tangent to a circle. The tangent to a circle forms a 90° angle with the radius at the point of tangency. Therefore, angle 𝑃𝐴𝐵 = 90°.

Step 3: Calculate angle 𝐴𝐵𝐷. Since angles in a triangle add up to 180°, we can calculate angle 𝐴𝐵𝐷 = 180° - 90° - 39° = 51°.

Step 4: Calculate angle 𝐵𝐷𝐶. Again, since angles in a triangle add up to 180°, we can calculate angle 𝐵𝐷𝐶 = 180° - 103° - 51° = 26°.

Step 5: Calculate angle 𝐴𝐷𝐵. Since 𝐴𝐷 is a straight line, angle 𝐴𝐷𝐵 = 180° - 26° = 154°.

So, the size of angle 𝐴𝐷𝐵 is 154°.