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 \(115^\circ\).