The formula to use is
n = 360/E
where 
n = number of sides
E = measure of exterior angle
In our case, E = 15 so 
n = 360/E
n = 360/15
n = 24
This regular polygon has 24 sides
        
             
        
        
        
2: 2/3; 3: 3/4; 4: 1/4; 5: 1/3; 6: 1/4; 7: 4/5; 8: 5/6-3/6=1/3
        
             
        
        
        
A graphing calculator or spreadsheet program can do this for you. Below is a plot from the Desmos on-line graphing calculator.
 
        
             
        
        
        
Answer:
Mikhail's age is 25 years old
Step-by-step explanation:
Let's make an equation: Say Mikhail is x, so Gabby would be 2*x=2x
If the sum of their ages equals 75, then x+2x=75, and x=2x=3x, so 3x=75.
75/3=25
 
        
             
        
        
        
In a full rotation, 360°, a point on the edge of a gear would travel a distance equal to its circumference.  The circumference of a circle is:
C=2πr, and since we are only traveling 150°, we need to set up an appropriate ratio for circumference to the distance the point travels:
d/C=150/360
d=5C/12 and since C=2πr
d=10πr/12
d=5πr/12, and since r=4in
d=5*4π/12 in
d=20π/12 in
d=5π/3 in
d≈5.24 in (to nearest hundredth of an inch)