- The given angle of 72° is an interior angle of the regular pentagon at the center.
- Since a regular pentagon has congruent angles, each of its five interior angles is 72°.
- At each vertex where the star’s point meets the pentagon, the 72° pentagon angle and two adjacent angles from the star’s triangles form a straight line (180°).
- Therefore, the sum of the two star triangle angles at that vertex is 180° - 72° = 108°.
- Because the star is symmetric and the pentagon is regular, these two angles are equal: 108° ÷ 2 = 54°.
- Each of the five points of the star forms an isosceles triangle with two base angles of 54°.
- The apex angle at each star point is therefore 180° - 54° - 54° = 72°.
- The intersecting lines of the star create smaller triangles inside; each of these small triangles has angles of 36°, 72°, and 72°, derived from subtracting known angles in the larger structure.
- All angles in the star are thus either 36°, 54°, 72°, or 108°, depending on their position.
Parent Tip: Review the logic above to help your child master the concept of math puzzles brain teasers.
