What are the sum of angles of a heptagon nonagon and dodecagon?

Answer 1

The sum of the interior angles of a polygon is given by:

sum_interior_angles = (number_of_sides - 2) × 180°

A heptagon has 7 sides

→ sum_interior_angles_heptagon = (7 - 2) × 180° = 900°.

A nonagon has 9 sides

→ sum_interior_angles_nonagon = (9 - 2) × 180° = 1260°.

A dodecagon has 12 sides

→ sum_interior_angles_dodecagon = (12 - 2) × 180° = 1800°.

To find the interior angle of a regular polygon either:

a) divide their sum by the number of sides

b) find an exterior angle and subtract form 180°; the exterior angle of a regular polygon is given by exterior_angle = 360° ÷ number_of_sides

Using method (a) and the sums found above:

interior_angle_regular_heptagon = 900° ÷ 7 = 128 4/7° ≈ 128.57°

interior_angle_regular_nonagon = 1260° ÷ 9 = 140°

interior_angle_regular_dodecagon = 1800° ÷ 12 = 150°