1. The problem asks to find the size of angle AED and the value of x in a circle with points A, B, D, E on the circumference and point C outside. 2. Since AE = AD, triangle AED is isosceles, so angles opposite these equal sides are equal. 3. The formula for the exterior angle of a triangle is: $$\text{Exterior angle} = \text{Sum of opposite interior angles}$$ 4. The angle ABD is given as 110° and angle BDE as 40°. 5. To find angle AED, use the fact that the sum of angles in triangle AED is 180°: $$\angle AED + \angle ADE + \angle DAE = 180^\circ$$ Since \angle ADE = \angle DAE, let each be $\theta$: $$\angle AED + 2\theta = 180^\circ$$ 6. To find x, use the exterior angle theorem at point C: $$x = \angle ABD + \angle BDE = 110^\circ + 40^\circ = 150^\circ$$ This formula helps relate the exterior angle x to the known interior angles. q_count is 2 because there are two distinct questions (a and b).