Q: How many line of symmetry does a regular polygon with x sides have?

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It is a regular pentagon!

All polygon sides are segments of lines.

A kite, for example.A kite, for example.A kite, for example.A kite, for example.

An ISOSCELES TRiangle. The line of symmetry is from the angle of the two equal adjacent sides, to the mid-point of the NON-equal side.

This is not possible for a normal regular polygon. (A regular polygon has all equal angles and all equal sides. A normal polygon has no intersecting edges.)The smallest regular polygon is an equilateral triangle (a three sided polygon), whose exterior angle measure is twice the measure of its interior angle. A four-sided polygon (a square) has equal interior and exterior angle measures of 90⁰. Starting from a five-sided polygon, the exterior angle measure is smaller than the interior angle measure.Let's assume that the given information is true. So we need to verify it.Let's say that the interior angle of the regular polygon has a measure of x degrees, and the measure of the exterior angle of that polygon is 4x degrees.Since the sum of the interior and the exterior angles of the polygon is 180 degrees (a straight line), the interior angle is 36 degrees.4x + x = 1805x = 1805x/5 = 180/5x = 36The sum of the angles of a polygon = 180⁰(n - 2), where n is the number of the sides of the polygon.The measure of one of the angles of a polygon = 180⁰(n - 2)/n. Substituting the angle measure of 36⁰ into this formula, we have:36⁰ = 180⁰(n - 2)/n (multiply by n to both sides)36⁰n = 180⁰(n - 2)36⁰n = 180⁰n - 360⁰ (add 360⁰ and subtract 36⁰n to both sides)360⁰ = 144⁰n (divide by 144⁰ to both sides)2.5 = n !!That means that a such normal polygon does not exist.

Related questions

22

The two numbers are the same.

22

polygon!

All regular polygons do.

In any regular polygon with an odd number of sides, a straight line from a vertex to the mid-point of the opposite side is a line of symmetry. So, for a pentagon, the answer is 5.

A line segment would have rotational symmetry.

An isosceles trapezoid.

All regular polygons A polygon is symmetrical if its sides that cross the line of symmetry are halved by the line of symmetry and if the sides that do not cross the line of symmetry have the same positions in space, the same lengths, and the same angles with their neighboring sides as do the sides on the other side of the line of symmetry. The only symmetrical triangles are isosceles triangles (equilateral triangles are isosceles). The only symmetrical quadrilaterals are squares, rectangles, rhombi (the line of symmetry connects either pair of opposite corners), isosceles trapezoids, and kites.

The number of lines of symmetry in a polygon corresponds to the number of sides it has. If a polygon has n sides, then its symmetry will be n lines of symmetry and it will have one point of symmetry. A pentagon has five lines of symmetry, nonagon has 9, n-gon has n lines of symmetry, so on and so forth.

any regular polygon e.g a circle

The most obvious one is the square. But it seems to me thatit's true for any regular polygon with an even number of sides.