4. True or False: The exterior angle of a regular nonagon measures \( 40^{\circ} \). Falc. 5. What is the sum of interior angles of an octagon? 16. What is the sum of interior angles of a decagon? 17. The sum of the measure of exterlor angles of any regular polygon will always add up to 18. The sum of three of the interior angles of a pentagon is \( 420^{\circ} \). If the remaining angles ar each measure?

Let's address each of your questions one by one: 4. **True or False: The exterior angle of a regular nonagon measures \( 40^{\circ} \).** - **False.** The exterior angle of a regular polygon can be calculated using the formula \( \frac{360^\circ}{n} \), where \( n \) is the number of sides. For a nonagon (9 sides), the exterior angle is \( \frac{360^\circ}{9} = 40^\circ \). So, the statement is actually **True**. 5. **What is the sum of interior angles of an octagon?** - The sum of the interior angles of a polygon can be calculated using the formula \( (n - 2) \times 180^\circ \), where \( n \) is the number of sides. For an octagon (8 sides): \[ (8 - 2) \times 180^\circ = 6 \times 180^\circ = 1080^\circ. \] - So, the sum of the interior angles of an octagon is \( 1080^\circ \). 16. **What is the sum of interior angles of a decagon?** - Using the same formula for a decagon (10 sides): \[ (10 - 2) \times 180^\circ = 8 \times 180^\circ = 1440^\circ. \] - So, the sum of the interior angles of a decagon is \( 1440^\circ \). 17. **The sum of the measure of exterior angles of any regular polygon will always add up to:** - The sum of the exterior angles of any polygon, regular or irregular, is always \( 360^\circ \). 18. **The sum of three of the interior angles of a pentagon is \( 420^{\circ} \). If the remaining angles are equal, what is the measure of each?** - First, calculate the sum of the interior angles of a pentagon: \[ (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ. \] - If three angles sum to \( 420^\circ \), then the sum of the remaining two angles is: \[ 540^\circ - 420^\circ = 120^\circ. \] - If the remaining two angles are equal, each angle measures: \[ \frac{120^\circ}{2} = 60^\circ. \] - Therefore, each of the remaining angles measures \( 60^\circ \). If you have any further questions or need clarification, feel free to ask!