Crystal Math X: Rays
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Author Topic: Crystal Math X: Rays  (Read 223 times)
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excelsus
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« on: April 18, 2014, 05:26:19 PM »
The big square in the picture below is divided into 25 smaller squares.
Add up the measures of the angles ∠MAN, ∠MBN, ∠MCN, ∠MDN and ∠MEN.

Solve this question without using a calculator!



Additional question:
The length of the square/rectangle has been extended to infinity, including all its smaller squares within.
Rays are drawn in according to the sample above.
What's the sum of the measures of the angles ∠MAN, ∠MBN, ∠MCN ... ?
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True Federalist (진정한 연방 주의자)
Ernest
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« Reply #1 on: April 18, 2014, 09:21:38 PM »
The sum is 45 degrees. Assuming that you mean for the length of line segment AN to remain 5, then the limit of the infinite sum is 90 degrees approaching from below.  If you mean for the length of line segment AN to equal the number of angles in each partial sum as you increase the number of angles, then the sum of the angles is 45 degrees.
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