The sum of interior angles of a regular polygon is 1080°
a) Find the size of each exterior angle
Show me
We have a formula for the sum of the angles:
sum of angles = 180(n-2), where n is the number of sides
180(n-2) = 1080
solve for n , now you have the number of angles,
(hint: it is a very common polygon)
divide 1080 by that n to get the size of each angle.
In this case n = 8
All the Exterior Angles of a polygon add up to 360°
Each exterior angle = 360° / n
Each exterior angle = 360° / 8 = 45°
To find the size of each exterior angle of a regular polygon, you can use the formula:
Each Exterior Angle = 360° / Number of Sides
In this case, we are given the sum of the interior angles (1080°), but we need to calculate the number of sides first.
The formula to calculate the sum of the interior angles of a polygon is:
Sum of Interior Angles = (Number of Sides - 2) * 180°
From the given information, we have:
Sum of Interior Angles = 1080°
Setting up the equation:
1080° = (Number of Sides - 2) * 180°
Simplifying the equation:
1080° = 180° * (Number of Sides - 2)
Dividing both sides by 180°:
6 = Number of Sides - 2
Adding 2 to both sides:
Number of Sides = 8
Now that we know the number of sides is 8, we can calculate the size of each exterior angle:
Each Exterior Angle = 360° / Number of Sides
Each Exterior Angle = 360° / 8
Each Exterior Angle = 45°
Therefore, the size of each exterior angle is 45°.