Q: What is the sum of the interior angle of a pentagon and how do you show the work?

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It is: 180-interior angle = exterior angle

To work out the angle of any 'perfect shape' you use this formula: interior angle =((number of sides - 2) x 180)/ number of sides for an octagon: interior angle =((8-2) x 180 )/ 8 = 135 degrees

Each exterior angle 45 degrees Each interior angle 135 degrees

Interior and adjacent exterior angles form a straight line so exterior angle = 180 - interior angle. If you are satisfied with this reply please consider awarding a Recommended Point to the responder.

To work out the sum of all the interior angles of a shape, we use the formula: 180(n-2) In this formula, n = the number of sides the polygon has. This formula only works out the sum of the interior angles, so to finish it off, we divide the answer by n. The number you get from that is equal to one interior angle of the particular polygon you put in the formula. To work out the exterior angles, you need to know that: Exterior angle + interior angle = 180 degrees. So to get the exterior angle, all we have to do is take the interior angle from 180 degrees. Triangle: 180(3-2) = 180 degrees 180/3 = 60 degrees 180 - 60 = 120 degrees Interior angle: 60 degrees Exterior angle: 120 degrees Square: 180(4-2) = 360 degrees 360/4 = 90 degrees 180 - 90 = 90 degrees Interior angle: 90 degrees Exterior angle: 90 degrees Pentagon: 180(5-2) = 540 degrees 540/5 = 108 degrees 180 - 108 = 72 degrees Interior angle: 108 degrees Exterior angle: 72 degrees You could do this for a long time and check every single polygon up to a 360 sided shape, but that would take ages. If you think about it logically, we already know that: Triangle: Int angle = 60 degrees Ext angle = 120 degrees Integers? YES Square: Int angle = 90 degrees Ext angle = 90 degrees Integers? YES Pentagon: Int angle = 108 degrees Ext angle = 72 degrees Integers? YES Do that for as many as you can, and you'll get a decent idea of which ones do and which ones don't. Just a hint: The more sides a polygon has, the less chance that there'll be an integer for it's interior and exterior angles.

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It is: 180-interior angle = exterior angle

If each interior angle is 178 degrees then the regular polygon will have 180 sides.

To work out the angle of any 'perfect shape' you use this formula: interior angle =((number of sides - 2) x 180)/ number of sides for an octagon: interior angle =((8-2) x 180 )/ 8 = 135 degrees

Each exterior angle 45 degrees Each interior angle 135 degrees

Yes it does. Good work!

If the polygon has n sides (or vertices) each exterior angle is 360/n. Each interior angle = 180 - exterior angle = 180 - 360/n

Interior and adjacent exterior angles form a straight line so exterior angle = 180 - interior angle. If you are satisfied with this reply please consider awarding a Recommended Point to the responder.

To work out the sum of all the interior angles of a shape, we use the formula: 180(n-2) In this formula, n = the number of sides the polygon has. This formula only works out the sum of the interior angles, so to finish it off, we divide the answer by n. The number you get from that is equal to one interior angle of the particular polygon you put in the formula. To work out the exterior angles, you need to know that: Exterior angle + interior angle = 180 degrees. So to get the exterior angle, all we have to do is take the interior angle from 180 degrees. Triangle: 180(3-2) = 180 degrees 180/3 = 60 degrees 180 - 60 = 120 degrees Interior angle: 60 degrees Exterior angle: 120 degrees Square: 180(4-2) = 360 degrees 360/4 = 90 degrees 180 - 90 = 90 degrees Interior angle: 90 degrees Exterior angle: 90 degrees Pentagon: 180(5-2) = 540 degrees 540/5 = 108 degrees 180 - 108 = 72 degrees Interior angle: 108 degrees Exterior angle: 72 degrees You could do this for a long time and check every single polygon up to a 360 sided shape, but that would take ages. If you think about it logically, we already know that: Triangle: Int angle = 60 degrees Ext angle = 120 degrees Integers? YES Square: Int angle = 90 degrees Ext angle = 90 degrees Integers? YES Pentagon: Int angle = 108 degrees Ext angle = 72 degrees Integers? YES Do that for as many as you can, and you'll get a decent idea of which ones do and which ones don't. Just a hint: The more sides a polygon has, the less chance that there'll be an integer for it's interior and exterior angles.

The sum of the internal angles of a pentagon is 540 degrees.Here's how:**To find the sum of the internal/interior angles of a polygon there is a formula,(n - 2)180 where n is the number of sides.**n = 5 , a pentagon has 5 sides(n - 2)180(5 - 2)180(3)180540So a pentagon would have 540 degrees. If the formula is too complicated for you to remember, you can use a pattern: Add 180 degrees to the next shape. For example, a triangle has 180 degrees, a quadrilateral has 360 degrees, pentagon has 540, hexagon 720, etc. Each time you add a side you are adding 180 degrees.The sum of the internal angles of a pentagon is 540 degrees.540 degreesThe interior angles in a pentagon total 540 degreesThe sum of the interior angles of a polygon with n sides is equal to 180 x (n - 2). Therefore, the sum of the interior angles of a pentagon is equal to 180 x (5 - 2) = 180 x 3 = 540 degrees.108 degrees.You must work out the exterior angle first.To find exterior, you count the angles on the pentagon, which is 5.And divide it by 360 which you'd get 72 degrees.Now to find the interior, you know a straight line is 180 degrees, so 180 minus 72 which is 108.Viola!360 degreesI vote for 540 degrees.* * * * *There is no need to vote. It can be proven that the interior angles of a polygon with n sides add to (180*(n-2) degrees. For a pentagon that would be 180*(5-2) = 180*3 = 540 degrees.The 5 interior angles of a pentagon add up to 540 degreesTotal interior angles of a pentagon (360+180) = 540 degrees.A pentagon can be divided into a square and a triangle. The interior angles of a square are 360 and for a triangle are 180.540°The 5 interior angles add up to 540 degreesThey add up to 540 degrees540 degrees in total.108 degrees individually.540 degrees total. 108 degrees for each angle.(5-2)*180 = 540 degrees108o if a regular pentagon. Total is 540o irrespective of shape. (2n - 4) right angles.540 degreesYes that is correct because the interior angles of a 5 sided pentagon add up to 540 degrees.The 5 interior angles of a pentagon add up to 540 degrees

You have to measure it - or have a lot more information that is given in this question.

(360) / (180 - n) n= interior angle in this case it will work like this: 360/(180-120) 360/(60) 6, so the number of sides is six.

To work out the interior angle use this formula(n - 2)*180/nwhere n is the number of sidesso for an 18 sided shape it would be(18-2)*180/18 = 160.