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But you are right about the pattern of the sum of the interior angles. 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. So that would be one triangle there. 6-1 practice angles of polygons answer key with work today. One, two, and then three, four. Sir, If we divide Polygon into 2 triangles we get 360 Degree but If we divide same Polygon into 4 triangles then we get 720 this is possible? 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. We have to use up all the four sides in this quadrilateral.

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Why not triangle breaker or something? If the number of variables is more than the number of equations and you are asked to find the exact value of the variables in a question(not a ratio or any other relation between the variables), don't waste your time over it and report the question to your professor. So I'm able to draw three non-overlapping triangles that perfectly cover this pentagon. An exterior angle is basically the interior angle subtracted from 360 (The maximum number of degrees an angle can be). We just have to figure out how many triangles we can divide something into, and then we just multiply by 180 degrees since each of those triangles will have 180 degrees. Of course it would take forever to do this though. 6-1 practice angles of polygons answer key with work account. Want to join the conversation? We already know that the sum of the interior angles of a triangle add up to 180 degrees. With two diagonals, 4 45-45-90 triangles are formed. Now, since the bottom side didn't rotate and the adjacent sides extended straight without rotating, all the angles must be the same as in the original pentagon. But what happens when we have polygons with more than three sides? Of sides) - 2 * 180. that will give you the sum of the interior angles of a polygon(6 votes). 6 1 angles of polygons practice. And we already know a plus b plus c is 180 degrees.

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Actually, let me make sure I'm counting the number of sides right. 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. So three times 180 degrees is equal to what? 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.

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So our number of triangles is going to be equal to 2. That is, all angles are equal. And we know each of those will have 180 degrees if we take the sum of their angles. 6-1 practice angles of polygons answer key with work table. I can get another triangle out of that right over there. What are some examples of this? And I'll just assume-- we already saw the case for four sides, five sides, or six sides. So those two sides right over there. 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.

So the remaining sides are going to be s minus 4. But when you take the sum of this one and this one, then you're going to get that whole interior angle of the polygon. Which angle is bigger: angle a of a square or angle z which is the remaining angle of a triangle with two angle measure of 58deg. I actually didn't-- I have to draw another line right over here. You can say, OK, the number of interior angles are going to be 102 minus 2. These are two different sides, and so I have to draw another line right over here. 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.