Before watching the lecture I already knew about polygons. Some examples are triangles, quadrilaterals, pentagons, and hexagons. They have different numbers of sides, different number of triangles that can fit inside, and their sum of their interior angles. Triangles have three sides, one triangle can fit inside, and the sum of their interior angles is one hundred eighty. Quadrilaterals have four sides, two triangles can fit inside, and the sum is three sixty. Pentagons have five sides, they can fit three triangles inside, and the sum is five hundred forty. Lastly, hexagons have six sides, four triangles can fit inside, and the sum of their interior angles is seven hundred twenty. This is all that I knew about before watching the lecture.
After watching the lecture I learned about interior angles and exterior angles. The theorem for interior angles is the sum of interior angles of an n-gon is (n-2)180. The corollary is the measure of each interior angle of a regular n-gon is (n-2)180 divided by n. The exterior angle theorem is the sum of the exterior angles of a convex polygon, one angle each vertex, is 360. The corollary is the measure of each exterior angle of a regular n-gon is 360/n. You can use both of these to find may different things dealing with angle measurement in polygons. This is everything that I learned about after watching the lecture.
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Hello Amy! For your second question we have to find the measure of each exterior angle of a regular pentagon. So we know that a regular pentagon has five sides so from that we can say that all the interior angles and exterior angles are congruent. Then we will have 5 times each angle will give us 360. So then all we have to do is divide 360/5 and get x to equal 72.
ReplyDeleteFor your first question, so add all the angles together and set it equal to 360. So you have 4x+5+6x+5x+4+5x+2+2x+3x+3-4=360. Then you combine the like terms. So your left with 25x+10=360. Then you subtract the 10 to the 360 so you have 25x=350. Now divide by 25 and x=14. So the answer is Letter C.
ReplyDeleteOk im going to answer your first question. With the shape you have to set it to 360. So then with all the angles given you set that to 360. When you get all though numbers in the equation then you solve out to get 25x+10=360 then you minus the 10 to the other side and get 350 and 25x=350 then divide it to get x and get 14 for your answer.
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