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What is the sum of the interior angle measure of a 13-sided polygon?
The sum of the interior angle measure of a 13-sided polygon is 1980 degrees. It is solved by doing: 180(s-2) 180(13-2) 180(11) = 1980 degrees *s- meaning sides*
How many sides does a polygon have if the measure of each interior angle of a regular polygon is 169?
Suppose the polygon has n sides. Then sum of the interior angles is (n-2)*180 degrees. Also, each angle is 169 degrees so their sum is 169*n degrees. That is, 180*n - 360 = 169*n or 11*n = 360 which has no integer solution. And, since a polygon, regular or not, cannot have a fractional number of sides, the question does not have a valid answer.
What is the measure of the interior angles of a regular 11-gon?
It is about 147 degrees. (147.27o)Subtract 2 from the number of sides and multiply by 180 to see the sum of all the angles put together. Divide by the number of sides to get the measure of each angle by itself. That works for any number of sides as long as it's regular. So, 11-2=9 and 9*180=1620 and lastly 1620/11=147.272727As a side note, to get straight to the measure of each individual angle you could also use 180-(360/x) where x is the number of sides.In a regular 11-gon, sometimes called a hendecagon, each interior angle will be equivalent. The number of adjacent triangles that can be drawn inside a polygon of n sides is (n-2); for an 11-gon, that would be nine.The sum of the angles in a triangle is always 180º, so the sum of angles in a hendecagon will be (9*180) which equals 1620 degrees. Since all interior angles are equal, divide 1620º by 11 to obtain the measure of each interior angle, about 147.27 degrees.The also-equivalent exterior angle measurement is found by subtracting 147.27º from 180º -- each exterior angle is 32.73º.
How many sides does a regular polygon have with an exterior angle of 32.72?
exterior angle of regular polygon is always 360 divided by number of sides, so number of sides = 360 divided by exterior angle, in this case 360/32.72 ie 11.
How many sides has a regular polygon whose interior angle is 11 times its exterior angles?
The measure of an interior angle in degrees of a regular polygon of n sides is given by the formula: 180 x (n-2) / nThe measure of an exterior angle in degrees of a regular polygon of n sides is given by the formula: 360/nIf the interior angle is 11 times the exterior angle, then:180 (n-2)/n = 11 x 360/nthen: 180 n - 360 = 11 x 360, or180 n = 12 x 360that its solution gives n = 24Accordingly, the answer is that the number of sides of this polygon is 24
