How to find an angle in a polygon - Math

The equation to calculate the magnitude of an interior angle is , where is equal to the number of sides.

For our question, .

To find the angle of any regular polygon you find the number of sides, . In this example, .

You then subtract 2 from the number of sides yielding 5.

Take 5 and multiply it by 180 degrees to yield the total number of degrees in the regular heptagon.

Then to find one individual angle we divide 900 by the total number of angles, 7.

The answer is .

The sum of the exterior angles of any polygon, one per vertex, is . As each angle measures , just divide 360 by 1.5 to get the number of angles.

To find the angle of any regular polygon you find the number of sides , which in this example is .

You then subtract from the number of sides yielding .

Take and multiply it by degrees to yield a total number of degrees in the regular nonagon.

Then to find one individual angle we divide by the total number of angles .

The answer is .

The sum of the measures of the exterior angles of any polygon, one per vertex, is . In a regular polygon, all of these angles are congruent, so divide 360 by 17 to get the measure of one exterior angle:

The sum of the measures of the exterior angles of any polygon, one per vertex, is . In a regular polygon, all of these angles are congruent, so divide 360 by 23 to get the measure of one exterior angle:

The measure of each interior angle of a regular polygon with sides is . We can substitute to obtain the angle measure:

The easiest way to answer this is to note that, since an interior angle and an exterior angle form a linear pair - and thus, a supplementary pair - each exterior angle would have measure . Since 360 divided by the number of sides of a regular polygon is equal to the measure of one of its exterior angles, we are seeking such that

Solve for :

The polygon has 20 sides.

The equation to calculate the magnitude of an interior angle is , where is equal to the number of sides.

For our question, .

To find the angle of any regular polygon you find the number of sides, . In this example, .

You then subtract 2 from the number of sides yielding 5.

Take 5 and multiply it by 180 degrees to yield the total number of degrees in the regular heptagon.

Then to find one individual angle we divide 900 by the total number of angles, 7.

The answer is .

The sum of the exterior angles of any polygon, one per vertex, is . As each angle measures , just divide 360 by 1.5 to get the number of angles.

To find the angle of any regular polygon you find the number of sides , which in this example is .

You then subtract from the number of sides yielding .

Take and multiply it by degrees to yield a total number of degrees in the regular nonagon.

Then to find one individual angle we divide by the total number of angles .

The answer is .

The sum of the measures of the exterior angles of any polygon, one per vertex, is . In a regular polygon, all of these angles are congruent, so divide 360 by 17 to get the measure of one exterior angle:

The sum of the measures of the exterior angles of any polygon, one per vertex, is . In a regular polygon, all of these angles are congruent, so divide 360 by 23 to get the measure of one exterior angle:

The measure of each interior angle of a regular polygon with sides is . We can substitute to obtain the angle measure:

The easiest way to answer this is to note that, since an interior angle and an exterior angle form a linear pair - and thus, a supplementary pair - each exterior angle would have measure . Since 360 divided by the number of sides of a regular polygon is equal to the measure of one of its exterior angles, we are seeking such that

Solve for :

The polygon has 20 sides.

The equation to calculate the magnitude of an interior angle is , where is equal to the number of sides.

For our question, .

To find the angle of any regular polygon you find the number of sides, . In this example, .

You then subtract 2 from the number of sides yielding 5.

Take 5 and multiply it by 180 degrees to yield the total number of degrees in the regular heptagon.

Then to find one individual angle we divide 900 by the total number of angles, 7.

The answer is .

The sum of the exterior angles of any polygon, one per vertex, is . As each angle measures , just divide 360 by 1.5 to get the number of angles.

To find the angle of any regular polygon you find the number of sides , which in this example is .

You then subtract from the number of sides yielding .

Take and multiply it by degrees to yield a total number of degrees in the regular nonagon.

Then to find one individual angle we divide by the total number of angles .

The answer is .