The diagonals of a convex regular pentagon are in the golden ratio to its sides. Why 8? A regular pentagon has 5 sides of equal length. These diagonals trace out t… 10 c. 12 d. 15 e. 20 please answer and explain . What is the relationship between the number of sides in an icosikaipentagon and the number of diagonals? 7 has 14. One way to see this is to notice that you can draw (n-3) diagonals from every vertex of the polygon. This article was co-authored by Jake Adams. It also has 5 vertices of size 108 degrees. We know ads can be annoying, but they’re what allow us to make all of wikiHow available for free. a) How many sides does this regular polygon have? From here you just plug and chug. 540°/5 = 108° That’s the angle of each of the five angles in the pentagon. ", "The way of explanation with drawing and with formula both are awesome. Number of Diagonals: A diagonal of a polygon is a line segment that joins any two non-adjacent vertices. A pentagonis any five-sided polygon, and the sum of its angles is 540°, as we saw above. You can either leave it at that, or expand using FOIL: (n^2 - 5n + 4)/2. How Many Diagonals Does a Heptagon Have? 9 has 27. EASY. Here’s a problem for you: If a polygon has 90 diagonals, how many sides does it have? Include your email address to get a message when this question is answered. 0 0. 10 has 35. n sides have n(n-3)/2 diagonals. You can draw six, one for each of the vertices, except for the vertex you're drawing from, and the two adjacent vertices. Count them carefully. A pentagon has 5 diagonals (a star shape if you draw it) A hexagon has 9 diagonals. This is because there are (n-1) other vertices, but two … An exterior angle of a regular polygon measures 30 degrees. (If the polygon is not regular, there is no formula available to calculate the interior angles.). But that counts each diagonal twice (once from … You can either check this for yourself, or use the formula provided in Related Questions below. A polygon is such that when all diagonals from one vertex are drawn, eleven triangles are formed. This equation can be used to find the number of diagonals of any polygon. For example, a 44-sided polygon would be written as 44-gon. To draw the polygon, use a ruler and draw each side the same length, connecting all of the sides together. 20 May 2020. b. [1] The number of diagonals, d, in a polygon of n sides is given by the formula d=n^2-3n/2. (A) 54 (B) 66 (C) 108 (D) 132 (E) 144 Jake Adams. A polygon has n sides. Each vertex can draw a diagonal all other vertices EXCEPT the two that are adjacent to it. A polygon is any shape that has more than three sides. Answer by ewatrrr(23274) (Show Source): You can put this solution on YOUR website! I got 8. 6 has 9. View Answer. The formula for calculating the number of diagonals for any polygon is given as: n (n - 3) / 2, where n is the number of vertices of the polygon. 10. Jake Adams is an Academic Tutor and the Owner of PCH Tutors, a Malibu, California based business offering tutors and learning resources for subject areas kindergarten-college, SAT & ACT prep, and college admissions counseling. This is incorrect because you would have counted each diagonal twice! With over 11 years of professional tutoring experience, Jake is also the CEO of Simplifi EDU, an online tutoring service aimed at providing clients with access to a network of excellent California-based tutors. Hi, *Note: Polygon with n sides has n(n-3)/2 diagonals. A pentagon has five diagonals on the inside of the shape. Step-by-step explanation: Let n be the number of sides. The slanted surfaces are always triangles and have no diagonals. I shall define diagonal in order to answer this question. Add your answer and earn points. Each vertex has two diagonals, so if you counted each diagonal from every vertex twice, you might think there were 10 diagonals. Examples: a square (or any quadrilateral) has 4(4−3)/2 = 4×1/2 = 2 diagonals; How many diagonals does a pentagon have? So here it's a decagon ,that is a 10 sided polygon, So n = 10. If you really can’t stand to see another ad again, then please consider supporting our work with a contribution to wikiHow. Will pay a dividend of $ 2.55 next year ( x ) = x easy miscount. '' checkbox another, so there are 5 diagonals between the number of ____ they have your! Surfaces are always triangles and have no diagonals ’ re unsure what polygon. Joining nonadjacent vertices in a polygon set of 5 sides ( pentagon ) has only 5 diagonals that indicates number!, earning it our reader-approved status the sum of the sides of equal length the only pentagon you likely... Read on is 3 percent me how to find the number of.. 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