The sum of interior angles of a regular polygon is 1800\degree1800°1800, degree.
Find the measure of each interior angle of the polygon.
The sum of interior angles of a yours regular polygon is 1800°
Use property:
Sum of interior angles = ( n - 2 ) ∙ 180°
In this case sum of interior angles = 1800°
So:
( n - 2 ) ∙ 180° = 1800°
Divide both sides by 180°
n - 2 = 10
Add 2 to both sides
n = 12
If he sum of interior angles of a yours regular polygon is 1800° then interior angles are:
Sum of interior angles / number of sides
In this case interior angles are:
1800° / 12 = 150°
To find the measure of each interior angle of a regular polygon, we can use the formula:
Sum of Interior Angles = (n - 2) * 180°
where n is the number of sides of the polygon.
In this case, we are given that the sum of interior angles is 1800°. So we can set up the equation:
1800° = (n - 2) * 180°
Next, we can solve for n:
1800° = 180°n - 360°
1800° + 360° = 180°n
2160° = 180°n
n = 2160°/180°
n = 12
The regular polygon has 12 sides. Now, we can find the measure of each interior angle by dividing the sum of interior angles by the number of sides:
Measure of each interior angle = Sum of Interior Angles / Number of Sides
Measure of each interior angle = 1800° / 12
Measure of each interior angle = 150°
Therefore, the measure of each interior angle of the polygon is 150°.