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What you attempted to do is draw both diagonals. So let's say that I have s sides. And I am going to make it irregular just to show that whatever we do here it probably applies to any quadrilateral with four sides. I got a total of eight triangles.
And then, no matter how many sides I have left over-- so I've already used four of the sides, but after that, if I have all sorts of craziness here. And then, I've already used four sides. Is their a simpler way of finding the interior angles of a polygon without dividing polygons into triangles? Hope this helps(3 votes). So a polygon is a many angled figure. We can even continue doing this until all five sides are different lengths. Angle a of a square is bigger. So if I have an s-sided polygon, I can get s minus 2 triangles that perfectly cover that polygon and that don't overlap with each other, which tells us that an s-sided polygon, if it has s minus 2 triangles, that the interior angles in it are going to be s minus 2 times 180 degrees. 6-1 practice angles of polygons answer key with work and work. So maybe we can divide this into two triangles. So let's try the case where we have a four-sided polygon-- a quadrilateral. This is one, two, three, four, five.
Whys is it called a polygon? So I could have all sorts of craziness right over here. So one out of that one. So let me write this down.
So in general, it seems like-- let's say. A heptagon has 7 sides, so we take the hexagon's sum of interior angles and add 180 to it getting us, 720+180=900 degrees. Get, Create, Make and Sign 6 1 angles of polygons answers. And it seems like, maybe, every incremental side you have after that, you can get another triangle out of it. Learn how to find the sum of the interior angles of any polygon. 6-1 practice angles of polygons answer key with work and value. And then we'll try to do a general version where we're just trying to figure out how many triangles can we fit into that thing. Let me draw it a little bit neater than that. What if you have more than one variable to solve for how do you solve that(5 votes).
So let me make sure. Want to join the conversation? But clearly, the side lengths are different. So plus six triangles.
Did I count-- am I just not seeing something? And we know each of those will have 180 degrees if we take the sum of their angles. Of course it would take forever to do this though. As we know that the sum of the measure of the angles of a triangle is 180 degrees, we can divide any polygon into triangles to find the sum of the measure of the angles of the polygon. So if someone told you that they had a 102-sided polygon-- so s is equal to 102 sides. So that's one triangle out of there, one triangle out of that side, one triangle out of that side, one triangle out of that side, and then one triangle out of this side. K but what about exterior angles? Let's do one more particular example.
The way you should do it is to draw as many diagonals as you can from a single vertex, not just draw all diagonals on the figure. For a polygon with more than four sides, can it have all the same angles, but not all the same side lengths? And we also know that the sum of all of those interior angles are equal to the sum of the interior angles of the polygon as a whole. 6 1 practice angles of polygons page 72. 6 1 angles of polygons practice. I'm not going to even worry about them right now. So three times 180 degrees is equal to what? Let's experiment with a hexagon.
So plus 180 degrees, which is equal to 360 degrees. 180-58-56=66, so angle z = 66 degrees. The bottom is shorter, and the sides next to it are longer. Not just things that have right angles, and parallel lines, and all the rest. And I'll just assume-- we already saw the case for four sides, five sides, or six sides. Use this formula: 180(n-2), 'n' being the number of sides of the polygon. And in this decagon, four of the sides were used for two triangles. And to see that, clearly, this interior angle is one of the angles of the polygon. Actually, that looks a little bit too close to being parallel.