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1) Grogg draws an equiangular polygon with g sides, and Winnie draws an equiangular polygon with w sides, where g < w. If the exterior angle of Grogg's polygon is congruent to the interior angle of Winnie's polygon, find w.

 

2) The measures of the angles a 9-gon are in ratio 3 : 1 : 4 : 1 : 5 : 9 : 2 : 6 : 5. What is the number of degrees in the measure of the largest angle?

 

3) In concave equilateral pentagon ABCDE, Angle A is qual to Angle B is equal to 90 degrees. What is the degree measure of angle E?

 

4) Alex thinks 131 degrees are neat. What is the maximum number of interior angles of a convex n-gon that can have measure 131 degrees?

Guest Jan 18, 2018
 #1
avatar+87641 
+1

1) We are trying to find this :

 

Interior angle of Winnie's  =  Exterior angle of Grogg's

 

(w - 2)180 / w  =  360/g   simplify

 

(w - 2) / w  =  2/g

 

g/2  =  w / (w - 2)

 

g  = 2w/ (w - 2)      it's  clear that  w > 2

 

Possibilities :

 

w      g

3       6

4      4

6      3

 

The  answer in red is correct

 

Winnie' polygon is a hexagon and Grogg's is a equilateral triangle

 

So

 

w  = 6

 

 

cool cool cool

CPhill  Jan 18, 2018
 #2
avatar+87641 
+1

2) The measures of the angles a 9-gon are in ratio 3 : 1 : 4 : 1 : 5 : 9 : 2 : 6 : 5. What is the number of degrees in the measure of the largest angle?

 

The sum of the interior angles of a 9-gon   =  (9 - 2) * 180  =  7 * 180  = 1260°

 

So....the largest angle is given by

 

9 / [ 3 + 1 + 4 + 1 + 5 + 9 + 2 + 6 + 5 ]   *  1260  =

 

9/ 36  * 1260   =

 

(1/4) * 1260   = 

 

315°

 

 

 

cool cool cool

CPhill  Jan 18, 2018

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