Triangle Angles 866985

1. **Problem Statement:** Determine which statements about the angles of the given triangle and its exterior angles are true. 2. **Key Definitions:** - An **exterior angle** of a triangle is an angle formed by one side of the triangle and the extension of an adjacent side. - An **adjacent interior angle** is an interior angle next to an exterior angle, sharing a common side. - **Remote interior angles** are the two interior angles of the triangle that are not adjacent to a given exterior angle. 3. **Analyze each statement:** - a) Angle 1 is an exterior angle. - Since Angle 1 is formed outside the triangle by extending a side, **this is true**. - b) Angle 2 is an exterior angle. - Angle 2 is inside the triangle, so **false**. - c) Angle 4 is an exterior angle. - Angle 4 is outside the triangle formed by extending a side, so **true**. - d) Angle 7 is an adjacent interior angle. - Adjacent interior angles are inside the triangle next to an exterior angle. Angle 7 is inside and adjacent to an exterior angle, so **true**. - e) Angle 6 is an adjacent interior angle. It is adjacent to the exterior angle 4. - Angle 6 is inside the triangle and shares a side with exterior angle 4, so **true**. - f) Angles 6 and 8 are remote interior angles to the exterior angle 1. - Exterior angle 1 is adjacent to one interior angle; the other two interior angles are remote. Angles 6 and 8 are inside but only one is remote to angle 1. Since angle 8 is not adjacent to angle 1, **true**. - g) Angles 6 and 7 are remote interior angles to the exterior angle 2. - Angle 2 is interior, so it cannot have remote interior angles. **False**. - h) Angles 7 and 8 are remote interior angles to the exterior angle 4. - Exterior angle 4 is adjacent to angle 6, so remote interior angles are the other two interior angles 7 and 8. **True**. 4. **Final answers:** - True: a, c, d, e, f, h - False: b, g