Найти внешний угол к углу С

To find the exterior angle adjacent to angle \( C \) in the triangle, you can use the following rule:

1. Understanding Exterior Angles:

   • The exterior angle is equal to the sum of the two non-adjacent (remote) interior angles of the triangle.

2. Given Information:

   • \(\angle ABC = 115^\circ\)
   • We need to find \(\angle ACB\) and then the exterior angle.

3. Using the Triangle Angle Sum Property:

   • The sum of angles in a triangle is \(180^\circ\).

   \[ \angle CAB + \angle ABC + \angle ACB = 180^\circ \]

4. Calculate \(\angle ACB\):

   • Let's denote \(\angle CAB = x\) and \(\angle ACB = y\).
   • Substitute the known angles:

   \[ x + 115^\circ + y = 180^\circ \]

   \[ x + y = 180^\circ - 115^\circ = 65^\circ \]

5. Finding the Exterior Angle:

   • The exterior angle at \(\angle C\) is formed with the extension of side \(AB\).
   • The exterior angle is equal to \(180^\circ - \angle ACB\).

   Since \(x + y = 65^\circ\), \(\angle ACB\) is included in these angles, so the exterior angle equals \(115^\circ\) since it is the same as the included \(\angle ABC\).

Thus, the exterior angle adjacent to \(\angle C\) is \(115^\circ\).