WHY must an octagon add up to 1080° (in pictures)Because there are now 6 triangles in an octagon, it must add up to `6times180°=1080°` Show
 The octagon can be made from 6 triangles. Example 1 An equilateral octagon will have 8 equal internal angles and would be `1080^circ/8=135^circ` Each internal angle is 135°. But the interior angles would still add up to 1080°. More Info Each time we add a side (triangle to square, square to pentagon, pentagon to hexagon) we add another 180°. Triangle to octagon
The total internal angles of a heptagon = 1080° Now, divide the total internal angle by the number of corners. i.e. divide 1080° by 8. `1080^circ/8=135^circ`
More Info A polygon that has all sides of the same length and all angles of the same measure is called a regular polygon. The angle that lies inside a polygon is called the interior angles. Answer: It is a regular octagon.Let's see the solution step by step. Explanation: We have to solve this for a number of sides of the polygon(p). The formula for the sum of interior angles, of a regular polygon with p sides is, Sum = 180(p – 2). Put, sum of interior angles = 1080° (Given) 1080° = 180(p – 2). 1080° / 180 = (p – 2). 6 = (p – 2). p = 6 + 2 p = 8 Hence, the polygon that has 8 sides is called an octagon. The figure of a regular octagon is given below: Thus, it is a regular octagon that has the sum of the measure of the interior angles is 1080°.Now take a look at what you have. You should see six non-overlapping triangles stuck together to make an octagon. Notice how every angle in each of those triangles is part of one of the angles of the octagon. That means that if you add up all the angles in those six triangles, you'll get the total internal angle sum of the octagon. In this case, 6 x 180 = 1080; an octagon's internal angles add up to 1080 degrees. You can do this with any convex polygon, and by convex, I mean that all the internal angles are less than 180 degrees. If you do a little investigating, you'll find that the number of triangles is always two less than the number of sides. This is so regular that it's stated as a theorem: If a convex polygon has n sides, then its interior angle sum (S) is given by the following equation: With this equation, you can calculate the interior angle sum of polygons with 37 sides (6300 degrees), 73 sides (12,780 degrees), or even 100 sides (17,640 degrees) without knowing any other information. Why is an octagon 1080 degrees?An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees. Because the octagon is regular, all of its sides and angles are congruent. Thus, the measure of each angle is equal to the sum of its angles divided by 8.
Do the angles in an octagon add up to 1080?So, the sum of the interior angles of an octagon is 1080 degrees. All sides are the same length (congruent) and all interior angles are the same size (congruent).
What shapes interior angles add up to 1080?Hence, the polygon with interior angle sum as 1080 ° is an octagon.
What is the sum of interior angles of octagon?1080°
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Why is the sum of the interior angles of an octagon 1080?
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