SOLUTION: MTLYNOBIAC is a regular decagon. If the sides MT and LY are extended to meet at E, find the measure of angle E.

Question 472262: MTLYNOBIAC is a regular decagon. If the sides MT and LY are extended to meet at E, find the measure of angle E.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the exterior angle of a regular decagon is given by the equation:
EA = 360/N
where EA is the exterior angle and N is the number of sides.
This makes each exterior angle equal to 36 degrees (360/10).
The triangle formed by the intersection of MT and LY would therefore be called TEL.
Angle T and L of this triangle would be equal to 36 degrees each.
That would force angle E to be equal to 108 because the sum of the angles of a triangle is equal to 180 degrees.
the interior angle of the regular decagon is given by the equation:
IA = (180 * (n-2)) / n which becomes (180 * 8) / 10 which becomes 144 degrees.
this means that the exterior angle is equal to 180 - 144 = 36 degrees.
the numbers check out.
each exterior angle is equal to 36 degrees which forces angle E to 108 degrees.
a reference on the properties of a decagon is shown below:
http://www.mathopenref.com/decagon.html
Each exterior angle would be 36 degrees.
Those become the interior angles of the triangle formed by the intersection.

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