Sum Of Angles In Pentagon

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A polygon is any closed effigy with sides fabricated from straight lines. At each vertex of a polygon, there is both an interior and exterior angle, corresponding to the angles on the inside and outside of the closed figure. Understanding the relationships that govern these angles is useful in various geometrical problems. In particular, it is helpful to know how to calculate the sum of interior angles in a polygon. This tin can exist done using a elementary formula, or past dividing the polygon into triangles.

1. 1

2. 2

   Count the number of sides in your polygon. Call up that a polygon must take at least three straight sides.^[5]

   • For case, if yous want to know the sum of the interior angles of a hexagon, you would count 6 sides.

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3. 3

   Plug the value of $$ north {\displaystyle n} into the formula. Call back, ${\displaystyle due north}$ is the number of sides in your polygon.^[6]

4. 4

   Solve for $$ n {\displaystyle n} . To exercise this, subtract ii from the number of sides, and multiply the difference by 180. This will give yous, in degrees, the sum of the interior angles in your polygon.^[vii]

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1. i

   Describe the polygon whose angles yous need to sum. The polygon can take any number of sides and can be regular or irregular.

   • For instance, you lot might want to find the sum of the interior angles of a hexagon, then you would draw a vi-sided shape.

2. 2

   Choose one vertex. Label this vertex A.

   • A vertex is a betoken where two sides of a polygon meet.

3. 3

   Draw a straight line from Point A to each other vertex in the polygon. The lines should not cantankerous. You should create a number of triangles.

   • You practice not take to draw lines to the adjacent vertices, since they are already continued by a side.
   • For case, for a hexagon you should depict three lines, dividing the shape into 4 triangles.

4. iv

   Multiply the number of triangles y'all created by 180. Since there are 180 degrees in a triangle, by multiplying the number of triangles in your polygon by 180, you can discover the sum of the interior angles of your polygon.^[8]

   • For case, since you divided your hexagon into 4 triangles, yous would calculate ${\displaystyle 4\times 180=720}$ to observe a total of 720 degrees in the interior of your polygon.

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Add together New Question

• Question

  How practise I find a unmarried interior angle?

  

  Piece of work out what all the interior adds up to, and so divide past all the same many sides the shape has.

• Question

  How exercise I summate the number of sides of a polygon if the sum of the interior angles is 1080?

  

  Split up that sum by 180°, then add 2. In this example, 1080° / 180° = half-dozen. 6 + two = eight. The polygon has 8 sides.

• Question

  If two equilateral triangles are placed together to course a rhomb, how practice I summate the value of each interior angle of this rhombus, and how practice I notice the sum?

  

  In the rhombus yous describe, the 2 smaller interior angles would each be 60°, and the 2 larger interior angles would each exist 120°. Y'all wouldn't have to summate the angles. Simple inspection of the rhombus and the two triangles would show what the angles are, given that equilateral triangles take three sixty° angles. The sum is 60° + sixty° + 120° + 120°.

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Video

• Cheque your piece of work on a piece of paper using a protractor to sum the interior angles manually. When doing this, be careful while drawing the polygon's sides as they should be linear.

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Things You'll Need

• Pencil
• Newspaper
• Protractor (optional)
• Pen
• Eraser
• Ruler

About This Article

Article Summary X

To summate the sum of interior angles, start past counting the number of sides in your polygon. Next, plug this number into the formula for the "n" value. And then, solve for "n" by subtracting two from the number of sides and multiplying the difference by 180. This will give you, in degrees, the sum of the interior angles in your polygon! To learn how to calculate the sum of interior angles by drawing triangles, read on!

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Sum Of Angles In Pentagon,

Source: https://www.wikihow.com/Calculate-the-Sum-of-Interior-Angles

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