In the following regular hexagon, which is 6m + 2n?

The vertex angles  of a regular hexagon  each measure 120°

Therefore,

3m + 40  = 120               2n - 30 = 120      

3m  = 80                         2n =  150

So                                    

6m  = 160

So 

6m + 2n  =

160  + 150  =

310°

Second one

Let the side of the pentagon  = x

Let the side of the hexagon  = y

So

3x  = 2y    ⇒     3x - 2y  = 0      (1)

x + y  = 10  ⇒  2x + 2y = 20    (2)

Add (1) and (2)  and we have that

5x  = 20

x  = 4

And   x + y  =10....so y  = 6

So

4BC + 5PQ  =

4x + 5y  =

4(4) + 5(6)  =

46