High college Math aid » Geometry » plane Geometry » various other Polygons » exactly how to uncover an angle in a polygon   Explanation:

The equation to calculation the size of an internal angle is , where is same to the number of sides.

You are watching: Calculate the measure of one angle in a regular nonagon

For ours question, . Explanation:

To discover the angle of any kind of regular polygon you uncover the variety of sides, . In this example, .

You then subtract 2 indigenous the variety of sides yielding 5.

Take 5 and multiply that by 180 degrees to productivity the total number of degrees in the continual heptagon. Then to discover one individual edge we division 900 by the total number of angles, 7.  .

A continuous polygon v sides has exterior angles that measure up each. How plenty of sides go the polygon have?

Explanation:

The amount of the exterior angles of any polygon, one every vertex, is . Together each angle actions , simply divide 360 by 1.5 to get the variety of angles. Explanation:

To discover the edge of any regular polygon you find the number of sides , i m sorry in this instance is .

You climate subtract from the number of sides yielding .

Take and main point it by degrees to yield a total number of degrees in the consistent nonagon. Then to uncover one individual angle we division by the total number of angles . The price is .

What is the measure of one exterior edge of a constant seventeen-sided polygon (nearest tenth the a degree)?

Explanation:

The sum of the procedures of the exterior angles of any polygon, one every vertex, is . In a regular polygon, all of these angles space congruent, so division 360 by 17 to acquire the measure of one exterior angle: What is the measure of one exterior angle of a constant twenty-three-sided polygon (nearest tenth of a degree)?

Explanation:

The sum of the actions of the exterior angle of any type of polygon, one per vertex, is . In a continuous polygon, every one of these angles are congruent, so division 360 through 23 to gain the measure up of one exterior angle: What is the measure up of one internal angle of a continual twenty-three-sided polygon (nearest tenth of a degree)?

Explanation:

The measure up of each interior angle the a continual polygon with sides is . We deserve to substitute to achieve the edge measure: Explanation:

The easiest way to prize this is to keep in mind that, since an inner angle and also an exterior angle kind a direct pair - and also thus, a supplementary pair - each exterior edge would have actually measure . Because 360 split by the variety of sides that a consistent polygon is equal to the measure of one of its exterior angles, we are seeking such that Solve for :    The polygon has actually 20 sides.

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