Interior & exterior angles

Calculate the sum of interior angles of a regular decagon (10 sides)

10 sides, so 8 triangles, so 8 x 180 degrees = 1440 degrees

Each exterior angle of a regular polygon is 14.4 degrees. How many sides does the shape have?

360 degrees (around the shape) divided by 14.4 degrees = 25. So the shape has 25 sides.

Each exterior angle of a regular polygon is 22.5 degrees. How many sides does the shape have?

360 degrees (around the shape) divided by 22.5 degrees = 16. So the shape has 16 sides.

Each exterior angle of a regular polygon is 7.5 degrees. How many sides does the shape have?

360 degrees (around the shape) divided by 7.5 degrees = 48. So the shape has 48 sides.

Each exterior angle of a regular polygon is 9 degrees. How many sides does the shape have?

360 degrees (around the shape) divided by 9 degrees = 40. So the shape has 40 sides.

The sum of the interior angles of a polygon is 4140 degrees. How many sides does the shape have?

4140 degrees divided by 180 degrees = 23. So the shape has 23 triangles within it and therefore has 25 sides (23 plus 2).

The sum of the interior angles of a regular polygon is 540 degrees. What is the size of each exterior angle?

540 degrees divided by 180 degrees = 3. So the shape has 3 triangles within it and therefore has 5 sides (3 plus 2). 360 degrees (around the shape) divided by 5 = 72 degrees.

The sum of the interior angles of a polygon is 5580 degrees. How many sides does the shape have?

5580 degrees divided by 180 degrees = 31. So the shape has 31 triangles within it and therefore has 33 sides (31 plus 2).

Calculate the sum of interior angles of a regular heptagon (7 sides)

7 sides, so 5 triangles, so 5 x 180 degrees = 900 degrees

The sum of the interior angles of a regular polygon is 720 degrees. What is the size of each exterior angle?

720 degrees divided by 180 degrees = 4. So the shape has 4 triangles within it and therefore has 6 sides (4 plus 2). 360 degrees (around the shape) divided by 6 = 60 degrees.

How many degrees in one interior angle of a regular octagon (8 sides)

8 sides, so 6 triangles, so 6 x 180 degrees = 1080 degrees in total.

What is the size of an interior angle on a regular 12 sided shape?

Either: 12 sides, so 10 triangles, so 10 x 180 degrees = 1800 degrees in total. 1800 degrees divided by 12 = 150 degrees (for each interior angle) Or, Interior angle and exterior angle add to 180 degrees, so, each exterior angle is 360 degrees divided by 12 = 30 degrees. 180 degrees - 30 degrees = 150 degrees.

What is the size of an interior angle on a regular 15 sided shape?

Either: 15 sides, so 13 triangles, so 13 x 180 degrees = 2340 degrees in total. 2340 degrees divided by 15 = 156 degrees (for each interior angle) Or, Interior angle and exterior angle add to 180 degrees, so, each exterior angle is 360 degrees divided by 15 = 24 degrees. 180 degrees - 24 degrees = 156 degrees.

What is the size of an exterior angle on a regular 20-sided shape?

Either: 360 degrees (around the shape) divided by 20 = 18 degrees, or, 20 sides, so 18 triangles, so 18 x 180 degrees = 3240 degrees in total. 3240 degrees divided by 20 = 162 degrees (for each interior angle) Interior angle and exterior angle add to 180 degrees, so 180 degrees - 162 degrees = 18 degrees.

Calculate the exterior angle of a regular nonagon (9 sides)

Either: 360 degrees (around the shape) divided by 9 = 40 degrees, or, 9 sides, so 7 triangles, so 7 x 180 degrees = 1260 degrees in total. 1260 degrees divided by 9 = 140 degrees (for each interior angle) Interior angle and exterior angle add to 180 degrees, so 180 degrees - 140 degrees = 40 degrees.

What is the size of an exterior angle on a regular 18-sided shape?

Either: 360 degrees (around the shape) divided by 18 = 20 degrees, or, 18 sides, so 16 triangles, so 16 x 180 degrees = 2880 degrees in total. 2880 degrees divided by 20 = 160 degrees (for each interior angle) Interior angle and exterior angle add to 180 degrees, so 180 degrees - 160 degrees = 20 degrees.