Help how do I find "one exterior angle 180- interior angle" of 6,7, 9, 12 sides please show your work so I can understand thank you
anyone????
If there are n sides, then each exterior angle is 360/n degrees.
each interior angle is thus 180 - 360/n = 180(n-2)/n degrees.
To find the measure of one exterior angle of a polygon, you need to use the formula:
Exterior angle = 360 degrees ÷ Number of sides
First, let's find the measure of one interior angle. To do this, we can use the formula:
Interior angle = (Number of sides - 2) × 180 degrees ÷ Number of sides
For a 6-sided polygon (hexagon):
Interior angle = (6 - 2) × 180 degrees ÷ 6
Interior angle = 4 × 180 degrees ÷ 6
Interior angle = 720 degrees ÷ 6
Interior angle = 120 degrees
Now, let's find the measure of one exterior angle of the hexagon:
Exterior angle = 360 degrees ÷ 6
Exterior angle = 60 degrees
For a 7-sided polygon (heptagon):
Interior angle = (7 - 2) × 180 degrees ÷ 7
Interior angle = 5 × 180 degrees ÷ 7
Interior angle = 900 degrees ÷ 7
Interior angle ≈ 128.571 degrees (rounded to 3 decimal places)
Now, let's find the measure of one exterior angle of the heptagon:
Exterior angle = 360 degrees ÷ 7
Exterior angle ≈ 51.429 degrees (rounded to 3 decimal places)
For a 9-sided polygon (nonagon):
Interior angle = (9 - 2) × 180 degrees ÷ 9
Interior angle = 7 × 180 degrees ÷ 9
Interior angle = 1,260 degrees ÷ 9
Interior angle ≈ 140 degrees (rounded to the nearest whole degree)
Now, let's find the measure of one exterior angle of the nonagon:
Exterior angle = 360 degrees ÷ 9
Exterior angle ≈ 40 degrees (rounded to the nearest whole degree)
For a 12-sided polygon (dodecagon):
Interior angle = (12 - 2) × 180 degrees ÷ 12
Interior angle = 10 × 180 degrees ÷ 12
Interior angle = 1,800 degrees ÷ 12
Interior angle = 150 degrees
Now, let's find the measure of one exterior angle of the dodecagon:
Exterior angle = 360 degrees ÷ 12
Exterior angle = 30 degrees
Therefore, the measures of one exterior angle for the given polygons are:
- Hexagon: 60 degrees
- Heptagon: approximately 51.429 degrees
- Nonagon: approximately 40 degrees
- Dodecagon: 30 degrees