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The ratios of the measures of an interior angle to an exterior angle of a regular polygon is 4 to 1 How many sides does the polygon have?
Answer: 10 sidesInterior angle = (180 * (number_of_sides - 2)) / number_of_sides Interior angle = 180 * (10-2) / 10 = 180 * 8 / 10 = 144Exterior angle = 360 / number_of_sides = 360 / 10 = 36 degreesRatio (144:36 = 4:1)Definitions:The exterior angle (e) is the angle created from the side and the imaginary line that would be if the adjacent side were to be extended beyond the vertices. The interior angle (i) plus the exterior angle (e) add up to 180 degrees, so i + e = 180. In a normal polygon, the sum of the exterior angle of all vertices adds up to 360 degrees; the sides do not overlap or cross. In a regular polygon each external angle is the same, and will divide evenly into 360 degrees to give the number of sides (n): 360 / e = n.Proof:Given that the ratio of the two angles is 4 to 1: i = 4e. Now substitute: i + e = 180; 4e + e = 5e = 180.e = 180 / 5 = 36 degrees.i = 180 - e = 144 degrees.360/e = 360/36 = 10 sides.The interior angle of a regular normal polygon of n sides is: i = (n-2)*180/n.For n=10: i = (10-2)*180/10 = 8*18 = 144 degrees, so it checks.Other i to e ratios:1 to 2: 3 sides: triangle (trigon) 2 to 2: 4 sides: tetrahedron (tetragon, square)3 to 2: 5 sides: pentahedron (pentagon)4 to 2: 6 sides: hexahedron (hexagon)5 to 2: 7 sides: heptahedron6 to 2: 8 sides: octahedron (octagon)7 to 2: 9 sides: enneahedron (nonogon)8 to 2: 10 sides: decahedron (decagon)
What is the name of the regular polygon whose interior angle is treble its exterior angle?
Interior angle = 3 x exterior angle. Hence Int Ang + Ext Ang = 180 Substituting 3 x Ext + Ext = 180 4 Ext = 180 Ext Angle = 180 / 4 = 45 degrees. And Exterior Ang;e = 360 / number of sides. number of sides = 360/ exterior angle No. of sides = 360/45 = 8 Hence the number of sides of the polygon is '8' . It is named as an OCTAGON.
How many sides would a polygon have if the angles added up to 172 degrees?
It wouldn't exist if the angles added up to 172o: the minimum sum for the angles of a polygon is that of a triangle, 180o - all the polygons with more sides are multiples of this, namely 4 sides => sum is 360o, 5 sides => sum is 540o, etc.If you mean:How many sides would a polygon have if all the angles were 172 degrees?then the answer is 45 sides.For all polygons:exterior_angle + interior_angle = 180osum_of_exterior_angles = 360oFor a regular polygon:number_of_sides x size_of_one_interior_angle = 360oInterior angle = 1720 => exterior_angle = 8o=> number_of_sides = 360o / 8o = 45.E
What shape has triangle have no angle and no sides and end with a e?
line
What type of polygon is the block letter E?
It is not a polygon
Is a E a polygon?
No it is not. A polygon is a plane space enclosed by straight lines. A letter "E" does not enclose any space and so cannot be a polygon.
Area of regular polygons?
The distance from the center of a regular polygon to a side is called its apothem(a). Keep that in mind. The perimeter(p) of the polygon is the measurement of all its sides, or the measurement of one side x the number of sides when it comes to a regular polygon.To find the area of the polygon, use the following e formula.Area = 1/2 (a) x (p)You must use the full perimeter.
How do you find the number of sides when given the exterior angle?
first u meause the top then the bottom part of the angle. u shood get the rite anser. ho[e did helps x
Why does cris angle not do cris angle mind freak any more?
he is going to have i think a new "series" on a&e on august 4
In triangle DEF angle E is 3 times angle D and angle F is 9 less than angle E what is the measure of each angle?
D=27 E=81 F=72
Is a ticket shape a polygon?
Yes, approximately.I say approximately because strictly speaking a ticket is usually a 3-dimensional shape (unless it is an e-ticket). No matter how thin it is, it still has a thickness which makes it 3-d. A polygon is a 2-d object.
What angle does the letter E have?
it has a right angle in there
