Difference between revisions of "Mock AIME 6 2006-2007 Problems/Problem 2"

(Created page with "==Problem == Draw in the diagonals of a regular octagon. What is the sum of all distinct angle measures, in degrees, formed by the intersections of the diagonals in the int...")
 
Line 4: Line 4:
  
 
==Solution==
 
==Solution==
{{Solution}}
+
 
 +
Each diagonal will have an angle with the horizontal base of the octagon as <math>22.5k</math> where <math>k=0,1,\cdots 7</math>
 +
{{alternate solution}}

Revision as of 18:08, 26 November 2023

Problem

Draw in the diagonals of a regular octagon. What is the sum of all distinct angle measures, in degrees, formed by the intersections of the diagonals in the interior of the octagon?

Solution

Each diagonal will have an angle with the horizontal base of the octagon as $22.5k$ where $k=0,1,\cdots 7$ Template:Alternate solution