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avatar+1685 

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

A. 325 degrees

B. 310 degrees

C. 295 degrees

D. 340 degrees

 

 

 

 

 

 

 

In a regular pentagon ABCDE and regular hexagon MNOPQR, 3CD = 2PQ and CD + QR = 10. Which is 4BC + 5PQ?

 

A. 46

B. 42

C. 44

D. 40

 Jan 16, 2020
 #1
avatar+109739 
+2

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°

 

 

cool cool cool

 Jan 16, 2020
 #2
avatar+109739 
+2

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

 

 

cool cool cool

 Jan 16, 2020

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