find the sum of the interior and exterior angles of a polygon of 7 sides.
find the measure of the exterior and interior angles of a regular pentagon.
To find the sum of the interior angles of a polygon with 'n' sides, you can use the formula:
Sum of Interior Angles = (n - 2) * 180 degrees.
For a polygon with 7 sides, the sum of the interior angles would be:
Sum of Interior Angles = (7 - 2) * 180 degrees = 5 * 180 degrees = 900 degrees.
To find the sum of the exterior angles of a polygon, you can use the formula:
Sum of Exterior Angles = 360 degrees.
For a polygon with 7 sides, the sum of the exterior angles would be:
Sum of Exterior Angles = 360 degrees.
To find the measure of each interior angle in a regular polygon, you can use the formula:
Measure of Interior Angle = Sum of Interior Angles / Number of Sides.
For a regular pentagon (a polygon with 5 sides), the measure of each interior angle would be:
Measure of Interior Angle = 900 degrees / 5 = 180 degrees.
To find the measure of each exterior angle in a regular polygon, you can use the formula:
Measure of Exterior Angle = 360 degrees / Number of Sides.
For a regular pentagon (a polygon with 5 sides), the measure of each exterior angle would be:
Measure of Exterior Angle = 360 degrees / 5 = 72 degrees.
To find the sum of the interior and exterior angles of a polygon of n sides, you can use the following formulas:
1. Sum of Interior Angles: The sum of the interior angles of a polygon with n sides can be calculated using the formula: (n - 2) * 180 degrees.
2. Sum of Exterior Angles: The sum of the exterior angles of any polygon is always 360 degrees.
Now let's apply these formulas to answer your questions:
1. Polygon with 7 sides:
The sum of the interior angles of a polygon with 7 sides can be calculated as: (7 - 2) * 180 degrees = 5 * 180 degrees = 900 degrees.
The sum of the exterior angles of any polygon is always 360 degrees.
Therefore, the sum of the interior angles of the polygon with 7 sides is 900 degrees, and the sum of the exterior angles is 360 degrees.
2. Regular pentagon:
A regular polygon has all sides and angles equal.
In the case of a regular pentagon (a polygon with 5 sides), we can find the measure of each interior and exterior angle.
To calculate the measure of the interior angle of a regular pentagon, we can use the formula: (n - 2) * 180 / n, where n is the number of sides.
In this case, the interior angle of a regular pentagon is: (5 - 2) * 180 / 5 = 3 * 180 / 5 = 540 / 5 = 108 degrees.
Since the sum of the interior angles of a pentagon is 540 degrees, and there are 5 interior angles, each interior angle of a regular pentagon measures 108 degrees.
To find the exterior angle of a regular pentagon, we subtract the interior angle from 180 degrees.
So the exterior angle of a regular pentagon is: 180 degrees - 108 degrees = 72 degrees.
Therefore, each interior angle of a regular pentagon measures 108 degrees, and each exterior angle measures 72 degrees.