Thread: pentagon

Let A=(0,0), B=(7,2), C=(3,4), D=(3,7) and E=(-1,5). Cameron walks the polygonal path ABCDEA, writing down the number of degrees turned at each corner. What is the sum of these five numbers? Notice that ABCDE in not a convex pentagon.

I got 491.(using a protractor) Could someone take a look at my attached work?
oops, on my last line of attached work i meant if angle c was convex

Why does convexity make any difference? Don't you have to end up where you started and facing the direction you started?

Hi Veronica 1999,
I calculated the angle of the first turn at B to be 137.5. At C 116.6and 116.6 at D.Finish and let me know if you get the right answer


bjh

TKHunny is suggesting a more theoretical approach, with which I agree. Are we explicitly calculating each angle as a means of verification?

Hello, Veronica1999!

While sketching, I found the problem more complex than anticipated.

Code:

      |         D
      |         o
      |   Y     *
      |     . β *
      |       . *
      |         o                 X
      |        C  *           .
      |             *  α  .
      |               o
      |           *    B
      |       *
      |   *
    A o - - - - - - - - - - - - -
      |

When he walks from to , he is walking in the direction

To walk to , he turns through . . . not


Then he walks from to , in the direction

To walk to , he turns through


And so on . . .

I had the right idea but made a mistake in the turn at C I recalculated all the turns with the following results 137,5,63.5,116.5,74.5, 85.35.Is this correct?