Answer: ∠1 = 52°, ∠4 = 40°, ∠7 = 100°, ∠10 = 49°, ∠13 = 65°
Explanation:
There are three formulas you need to find the angles. Each formula is based on where the vertex lies.
On the circle: Measure of the angle = (1/2) the arc 
∠4 = (1/2)°80 ∠10 = (1/2)(18° + 80°) ∠13 = (1/2)130°
 = 40° = (1/2)98° = 65°
 = 49°
Inside the circle: (1/2) Sum of the Big arc and Little Arc 
∠7 = (1/2) (130° + 70°)
 = (1/2)200°
 = 100°
Outside the circle: (1/2) Difference of the Big arc and Little Arc 
∠1 = (1/2)[(62° + 130°) - (70° + 18°)]
 = (1/2) (192° - 88°)
 = (1/2)104°
 = 52°
Below is the solution for ALL of the angles