And to generalize it, let's realize that just to get our first two triangles, we have to use up four sides. I'm not going to even worry about them right now. 6 1 angles of polygons practice. 6-1 practice angles of polygons answer key with work sheet. Maybe your real question should be why don't we call a triangle a trigon (3 angled), or a quadrilateral a quadrigon (4 angled) like we do pentagon, hexagon, heptagon, octagon, nonagon, and decagon. That would be another triangle. And so there you have it. So let me draw it like this.
So maybe we can divide this into two triangles. Same thing for an octagon, we take the 900 from before and add another 180, (or another triangle), getting us 1, 080 degrees. 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. 300 plus 240 is equal to 540 degrees. I have these two triangles out of four sides. So a polygon is a many angled figure. Let me draw it a little bit neater than that. 6-1 practice angles of polygons answer key with work together. Hexagon has 6, so we take 540+180=720. So our number of triangles is going to be equal to 2. Plus this whole angle, which is going to be c plus y. Hope this helps(3 votes). Now remove the bottom side and slide it straight down a little bit. You have 2 angles on each vertex, and they are all 45, so 45 • 8 = 360. So if someone told you that they had a 102-sided polygon-- so s is equal to 102 sides.
I can get another triangle out of that right over there. And it seems like, maybe, every incremental side you have after that, you can get another triangle out of it. So it'd be 18, 000 degrees for the interior angles of a 102-sided polygon. So the number of triangles are going to be 2 plus s minus 4. So let me write this down. So I think you see the general idea here. Let's experiment with a hexagon. Orient it so that the bottom side is horizontal. And we know that z plus x plus y is equal to 180 degrees. And in this decagon, four of the sides were used for two triangles. 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. So four sides used for two triangles. 6-1 practice angles of polygons answer key with work and answers. So if you take the sum of all of the interior angles of all of these triangles, you're actually just finding the sum of all of the interior angles of the polygon. What if you have more than one variable to solve for how do you solve that(5 votes).
Which is a pretty cool result. Want to join the conversation? Extend the sides you separated it from until they touch the bottom side again. With a square, the diagonals are perpendicular (kite property) and they bisect the vertex angles (rhombus property). I actually didn't-- I have to draw another line right over here. Of course it would take forever to do this though. This is one triangle, the other triangle, and the other one. But what happens when we have polygons with more than three sides? Actually, let me make sure I'm counting the number of sides right. Of sides) - 2 * 180. that will give you the sum of the interior angles of a polygon(6 votes). That is, all angles are equal. Get, Create, Make and Sign 6 1 angles of polygons answers. So I have one, two, three, four, five, six, seven, eight, nine, 10.
The first four, sides we're going to get two triangles. Does this answer it weed 420(1 vote). 2 plus s minus 4 is just s minus 2. Take a square which is the regular quadrilateral. It looks like every other incremental side I can get another triangle out of it. They'll touch it somewhere in the middle, so cut off the excess. Imagine a regular pentagon, all sides and angles equal. You could imagine putting a big black piece of construction paper. In a triangle there is 180 degrees in the interior. And then, I've already used four sides.
Please only draw diagonals from a SINGLE vertex, not all possible diagonals to use the (n-2) • 180° formula. Let's do one more particular example. Explore the properties of parallelograms! Find the sum of the measures of the interior angles of each convex polygon. And so if we want the measure of the sum of all of the interior angles, all of the interior angles are going to be b plus z-- that's two of the interior angles of this polygon-- plus this angle, which is just going to be a plus x. a plus x is that whole angle. Now let's generalize it. So let's say that I have s sides. There might be other sides here. Let's say I have an s-sided polygon, and I want to figure out how many non-overlapping triangles will perfectly cover that polygon. What you attempted to do is draw both diagonals. So we can use this pattern to find the sum of interior angle degrees for even 1, 000 sided polygons.