Sum of all the angles \( =(n-2) \times 180^{\circ} \). Each internal angle \( =( \) Sum of all the angles \( ) \div \mathrm{n}= \) number of sides or number of angles of a polygon] In a regular polygon with 6 sides, the sum of all the angles is and every internal angle measures In a regular polygon with 8 sides, the sum of all the angles is and every internal angle measures

To find the sum of all the angles and the measure of each internal angle for regular polygons, we can use the formulas you provided. ### For a regular polygon with 6 sides (hexagon): 1. **Sum of all the angles**: \[ \text{Sum of all angles} = (n-2) \times 180^{\circ} \] where \( n = 6 \): \[ \text{Sum of all angles} = (6-2) \times 180^{\circ} = 4 \times 180^{\circ} = 720^{\circ} \] 2. **Each internal angle**: \[ \text{Each internal angle} = \frac{\text{Sum of all angles}}{n} = \frac{720^{\circ}}{6} = 120^{\circ} \] ### For a regular polygon with 8 sides (octagon): 1. **Sum of all the angles**: \[ \text{Sum of all angles} = (n-2) \times 180^{\circ} \] where \( n = 8 \): \[ \text{Sum of all angles} = (8-2) \times 180^{\circ} = 6 \times 180^{\circ} = 1080^{\circ} \] 2. **Each internal angle**: \[ \text{Each internal angle} = \frac{\text{Sum of all angles}}{n} = \frac{1080^{\circ}}{8} = 135^{\circ} \] ### Summary: - In a regular polygon with 6 sides (hexagon): - The sum of all the angles is \( 720^{\circ} \). - Each internal angle measures \( 120^{\circ} \). - In a regular polygon with 8 sides (octagon): - The sum of all the angles is \( 1080^{\circ} \). - Each internal angle measures \( 135^{\circ} \).