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Seven points are evenly spaced out on a circle and connected as shown below to form a 7-pointed star. What is the sum of the angle measurements of the seven tips of the star, in degrees? One such angle is marked as \(\alpha\) below.

 

tertre  Mar 30, 2018
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 #1
avatar+85759 
+2

 

 

Notice, tertre, that  inscribed angle ACE  intercepts minor arc AE which measures  (3/7)  of the circumference of the circle  =  (3/7)(360° )

 

So.....the measure of    ACE  =  measure of α =  (1/2) of its  intercepted arc  =

 

(1/2)* (3/7) (360°)   =

 

(3 /14)(360°) 

 

So  7 times this  is  

 

(7)(3/14)(360°)   =

 

(3/2)(360°)  =   540°

 

 

cool cool cool

CPhill  Mar 30, 2018
 #2
avatar+2347 
+2

Oh, I get it now! Thanks so much!

tertre  Mar 30, 2018

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