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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
What relationship exist between the number of sides on a regular polygon and the number of lines of symmetry?
They are the same.
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 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.
