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|