A triangle has three corners, called vertices. The sides of a triangle that come together at a vertex form an angle. This angle is called the interior angle. In the picture below, the angles a, b and c are the three interior angles of the triangle. An exterior angle is formed by extending one of the sides of the triangle; the angle between the extended side and the other side is the exterior angle. In the picture, angle d is an exterior angle.
The exterior angle theorem says that the size of an exterior angle at a vertex of a triangle equals the sum of the sizes of the interior angles at the other two vertices of the triangle. So, in the picture, the size of angle d equals the size of angle a plus the size of angle c.
Given: In ∆ABC, angle ACD is the exterior angle.
To prove: m'ACD = m'ABC + mBAC (here, mACD denotes the size of the angle ACD)
|In ∆ABC, m'a + m'b + m'c = 180°------'''||Sum of the measures of all the angles of a triangle is 180°|
|Also, m'b + m'd = 180°-------||Linear pair axiom|
|∴ m'a + m'c + m'b = m'b + md||From  and |
| ∴ m'a + m'c + |
|∴ m'd = m'a + mc|
|i.e. m'ACD = m'ABC + mBAC|
US Patent Issued to Kite Image Technologies on Oct. 16 for "Method for Handwritten Character Recognition, System for Handwritten Character Recognition, Program for Handwritten Character Recognition and Storing Medium" (Japanese Inventors)
Oct 21, 2012; ALEXANDRIA, Va., Oct. 21 -- United States Patent no. 8,290,274, issued on Oct. 16, was assigned to Kite Image Technologies Inc....