How many sides does a polygon have if the maximum number of diagonals that you can draw inside it is 54?
12
So, the number of sides of a polygon which have 54 diagonals is 12.
How do you find the number of sides of a polygon if the diagonals are given?
By using the formula for the number of diagonals of a polygon with n sides, you can determine how many sides a polygon has if you know the number of diagonals it has. For example, if a polygon has 54 diagonals, find how many sides it has. Then, solve for n using algebra. First multiply both sides by 2.
How many sides does a polygon have if the sum of the interior angles is 3780?
A polygon with 23 sides has a total of 3780 degrees. total interior angles = (n – 2)180°, where n is the number of sides.
What is the sum of the angles of a polygon that has 20 diagonals?
In geometry, an icosagon or 20-gon is a twenty-sided polygon. The sum of any icosagon’s interior angles is 3240 degrees.
How many sides does a polygon have if it has 27 diagonals?
The polygon has 9 sides.
How many sides does a polygon have with 170 diagonals?
Another way to express the general rule for the total number of diagonals is to think about the number of diagonals that can be drawn from each vertex in a polygon. That is “3” less than the number of sides. Therefore, for a 20-sided polygon, there will be 190 lines and 170 diagonals.
How many diagonals are there in a polygon having 12 sides?
54 diagonals
There are 54 diagonals in a dodecagon. These diagonals can be calculated with the help of the formula: 1/2 × n × (n-3), where n = number of sides. In this case, n = 12.
How do you find the number of sides of a polygon with the sum of the interior angles?
Answer: To find the number of sides of a polygon when given the sum of interior angles, we use the formula: Sum of interior angles = (n – 2) × 180, where n is the number of sides.
What is the sum of the interior angles of a dodecagon?
1800°
Dodecagon/Sum of interior angles
How do you find the amount of diagonals in a polygon?
The number of diagonals in a polygon that can be drawn from any vertex in a polygon is three less than the number of sides. To find the total number of diagonals in a polygon, multiply the number of diagonals per vertex (n – 3) by the number of vertices, n, and divide by 2 (otherwise each diagonal is counted twice).
What is the sum of the exterior angles of a polygon?
The angle next to an interior angle, formed by extending the side of the polygon, is the exterior angle. Hence, we can say, if a polygon is convex, then the sum of the degree measures of the exterior angles, one at each vertex, is 360°. Therefore, the sum of exterior angles = 360°
How many diagonals does a polygon with 8 sides have?
discusses the relationship between the number of sides of the polygon and the sum of its interior angles. Once you find out that a polygon whose interior angles add up to 1080 degrees has 8 sides, you can reason that from each of the 8 corners you can draw 5 diagonals.
What are the characteristics of polygons?
Characteristics of Polygons Include: • They can have any number of sides and angles, but the sides can never be curved. • The sides of the polygons are called segments and the points where the segments intersect are called vertices.
How many triangles does a polygon have at each vertex?
So sum of all interior angles = (!80–36)*10 = 144*10 = 1440 deg. 1440/180 = 8. So at any one vertex we can draw 8 diagonals and thus form 8 triangles at each vertex. A regular polygon has 14 diagonals. how many sides does the polygon have?