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# PLS HELP NOW I AM DESPERATE

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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?

Jan 18, 2018

#1
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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   Jan 18, 2018
#2
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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°   Jan 18, 2018