1. The problem asks to find the measures of angles ABF, ABD, EBC, FBC, and DBG given the angles 110\degree, 65\degree, and 20\degree around point B where lines AC and ED intersect. 2. Using the given angles and the fact that angles around a point sum to 360\degree, we find: - Angle ABF = 110\degree (given) - Angle ABD = 65\degree (given) - Angle EBC = 20\degree (given) 3. To find angles FBC and DBG, note that the sum of all angles around B is 360\degree: $$110 + 65 + 20 + \text{Angle FBC} + \text{Angle DBG} = 360$$ $$195 + \text{Angle FBC} + \text{Angle DBG} = 360$$ $$\text{Angle FBC} + \text{Angle DBG} = 165$$ 4. Without additional information, assume angles FBC and DBG are equal: $$\text{Angle FBC} = \text{Angle DBG} = \frac{165}{2} = 82.5\degree$$ Final answers: - Angle ABF = 110\degree - Angle ABD = 65\degree - Angle EBC = 20\degree - Angle FBC = 82.5\degree - Angle DBG = 82.5\degree