Question

. If the measure of one interior angle of a regular polygon is 160°, find the number of sides.

Answer 1

To find the number of sides of a regular polygon when given the measure of one interior angle, divide 360 by the angle.

Step-by-step explanation:

A regular polygon is a polygon that has all sides of equal length and all angles are equal. In other words, it is a polygon with both sides and angles that are congruent (identical). The properties of regular polygons make them symmetrical and often aesthetically pleasing.

Key characteristics of a regular polygon:

Equal Side Lengths: All sides of a regular polygon are of the same length.

Equal Angles: All interior angles of a regular polygon are congruent (have the same measure).

Symmetry: Regular polygons are symmetric. If you draw lines from the center to the vertices, you'll find that these lines are symmetrical wit

To find the number of sides of a regular polygon when given the measure of one interior angle, we can use the formula:

n = 360 / angle

In this case, the measure of one interior angle is 160°, so we substitute it into the formula:

n = 360 / 160 = 2.25

Since the number of sides of a polygon must be a whole number, we can round 2.25 to the nearest whole number, which is 2. Therefore, the number of sides of the polygon is 2.

Answer 2

The number of sides of the regular polygon is 2.

Step-by-step explanation:

To find the number of sides of a regular polygon, we can use the formula:

Number of sides = 360° / Measure of one interior angle

In this case, the measure of one interior angle is given as 160°. Plugging this value into the formula, we have:

Number of sides = 360° / 160°

Simplifying this expression, we get:

Number of sides ≈ 2.25

Since the number of sides of a polygon must be a whole number, the closest whole number to 2.25 is 2. Therefore, the number of sides of the regular polygon is 2.