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Calculate the number of sides of a regular polygon whose interior angles are each 156 degrees?
Exterior angle = 180-156 = 24 degrees Number of sides = 360/24 = 15 sides. If you can't remember the formula, then remember this to help figure it out: The regular polygon can be divided into triangles (like pizza slices). Each triangle is an isosceles triangle and all of them are congruent (since it's a regular polygon). Take one of the triangles: each of the 'leg angles' will be half of the polygon angle (the leg of the triangle has bisected the polygon angle). So these two angles will add together to be the same measure as the polygon angle (call it Ap). So the other angle in the triangle is in the center and all these pizza slice angle make a circle in the middle (360°). Since the triangle sums to 180°, the angle in the middle is (180° - Ap), then you have: Number of sides = (360°) / (180° - Ap), or in this case: 360/(180-156) = 15 sides.
Does a polygon have more angles or sides explain?
A polygon has exactly the same number of both internal and external angles to the number of sides. Assuming external angles count, there are two times the number of sides as the total number of angles
Each interior angle if a regular polygon measurses 172 degrees how many sides does the polygon have?
The easiest way to solve this is to use the exterior angles of the polygon. The sum of an exterior angle and interior angle is 180o. Also the sum of all the exterior angles of a polygon is 360o. As the polygon is regular, all the interior angles are the same and all the exterior angles are the same. So, for an interior angle of 172o the exterior angle is 180-172 = 8o. The sum of all the exterior angles is 360o so how many 8o make up 360o? 360/8=45. Thus the polygon with interior angles of 172o has 45 sides.
What relationship exist between the number of sides on a regular polygon and the number of lines of symmetry?
They are the same.
What is a polygon with all sides the same length and all angles the same measure called?
A polygon with all sides the same length and all angles the same measure is called a regular polygon. Examples include triangles, squares, pentagons, and hexagons. When the number of sides approaches infinity, the shape of a circle is formed.
Is it possible for the interior angle of a regular polygon to be 154?
No. The sum of the exterior angles of a polygon sum to 360o For a regular polygon, they are all the same size ⇒ dividing 360o by the exterior angle gives the number of sides. Interior angle = 154o ⇒ exterior angle = 180o - 154o = 26o ⇒ number of sides = 360o ÷ 26o = 1311/13 sides But a polygon must have a whole number of sides ⇒ 154o cannot be the interior angle of a regular polygon.
Find the number of sides of a polygon if each interior angle is 180?
A polygon with each interior angle measuring 180 degrees is a regular octagon. In a regular octagon, all the sides are the same length and all the interior angles are the same. Therefore, since each interior angle is 180 degrees, the number of sides is 8. You can use the formula n - 2, where n is the number of sides, to find the number of sides for any regular polygon. In this case, n - 2 = 8 - 2 = 6. Since 6 is the number of sides, the polygon is an octagon.
Why does a polygon have the same number of sides and angles?
because every two lines form an angle
How do you find the measure of one angle in a polygon?
For a regular polygon the internal angle between two sides is (180 - (360/n)) degrees where n is the number of sides. A regular polygon is one where all side lengths and angles are the same.
If the number of sides of a regular polygon doubles what happens to the measure of each exterior angle?
They remain the same.
What is a polygon with the same sides and measurement?
The question is not sufficiently well defined: the answer depends on same as WHAT! A polygon with the same sides and angle measurements as the corresponding sides and angles of another polygon is a congruent polygon. A polygon in which all the sides are the same length and all the angles are of equal measure is a regular polygon.
Does a polygon have more angles or sides?
A polygon has exactly as many sides as it has angles.
What polygon has an angle of rotation of 180 degrees?
Consider an irregular polygon with an even number of sides - 2n. If the sides 1 and n+1 are of the same length, sides 2 and n+2, sides 3 and n + 3 etc and if the corresponding angles are the same, then the polygon will have a rotational symmetry of 180 degrees.
Does a polygon usually have more side or angle?
I think it has the same because it just depends on how to split number they're looking 4
Does e polygon have more sides or more angle?
It is the same 5 sides and 5 angles.
What is regulate polygon?
A regular polygon has sides of equal length and each interior angle is the same measure
How does the number of vertices of a polygon compare to the number of sides of the same polygon?
They are equal.
