You use the fact that the sum of the interior angles of a regular polygon with n sides is:
180(n-2) degrees
Now you have the sum of measures of all the interior angles so divide that by n and you have the measure of each interior angle.
To find the number of sides ( n ) of a regular polygon with an interior angle of 172 degrees, we can use the formula for the interior angle of a regular polygon: [ \text{Interior Angle} = \frac{(n-2) \times 180}{n} ] Setting this equal to 172 degrees gives: [ \frac{(n-2) \times 180}{n} = 172 ] Solving for ( n ), we find ( n = 22 ). Therefore, a regular polygon with an interior angle of 172 degrees has 22 sides.
360/number of sides and deduct the quotient from 180 which will give the measure of each interior angle
It is: (number of sides -2)*180 = sum of interior angles If its a regular polygon then: sum of interior angles/number of sides = each interior angle
To find the number of sides ( n ) of a polygon using its interior angle ( A ), you can use the formula for the interior angle of a regular polygon: ( A = \frac{(n-2) \times 180}{n} ). Rearranging this equation, you get ( n = \frac{360}{180 - A} ). By substituting the known value of the interior angle ( A ), you can calculate the number of sides ( n ) of the polygon.
75.32Improved Answer:-It is: 157.5 degrees
If its a regular polygon then 180-interior angle and divide the answer into 360 which will give the number of sides of the polygon.
a 7 sided polygon is heptagon and the interior angle of it is 128.57 degrees.
999999
To find the number of sides ( n ) of a regular polygon with an interior angle of 172 degrees, we can use the formula for the interior angle of a regular polygon: [ \text{Interior Angle} = \frac{(n-2) \times 180}{n} ] Setting this equal to 172 degrees gives: [ \frac{(n-2) \times 180}{n} = 172 ] Solving for ( n ), we find ( n = 22 ). Therefore, a regular polygon with an interior angle of 172 degrees has 22 sides.
40 sides
Each interior angle of the regular 8 sided octagon measures 135 degrees
It will have 10 equal sides
that's geometry so the formula to find the measure of each interior angle of a regular polygon is: Ia=stands for internal angle Ia=(n-2)180 ---------- n that's the formula.
Each interior angle: 140 degrees Each exterior angle: 40 degrees
The sum of a regular polygon's interior angles is always equal to (n-2) * 180, where n is the number of sides in the polygon. Given that one exterior angle measures 40 degrees, we can find the interior angle by subtracting 40 from 180 degrees (since the exterior and interior angles are supplementary) to get 140 degrees. So, the sum of the interior angles of the regular polygon is 140 * n.
180-interior angle = exterior angle If it's a regular polygon then: 360/number of sides = exterior angle
360/number of sides and deduct the quotient from 180 which will give the measure of each interior angle