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What is the total sum of its interior angles of a polygon that has 189 diagonals showing work?
Wiki User
∙ 8y ago
Using the diagonal formula when n is number of sides :-
If: 0.5*(n^2-3n) = 189
Then multiplying both sides by 2 and subtracting both sides by 2*189
So: n^2-3n-378 = 0
Solving the above quadratic equation gives n a positive value of 21
Sum of interior angles: (21-2)*180 = 3420 degrees
Wiki User
∙ 8y ago
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How many sides does a polygon have if the interior angles equal 180 degrees?
If all of the interior angles of the polygon add up to 180 degrees, then the polygon is a triangle.
What interior angles of a polygon has 22 sides?
The interior angles add up to 3600 degrees
Is a regular polygon a polygon with all sides congruent?
A regular polygon is a polygon with congruent sides and interior angles.
What is an exterior and interior angles?
The exterior and interior angles of each vertex of a polygon add up to 180 degrees.
Regular polygon with 174 degrees interior?
Your polygon has 60 sides. Total interior angles 116 x 90 = 10440 degrees. This works because interior angles of any n-sided polygon total (2n - 4 right angles or 180n - 360 degrees
What forms within a polygon shape?
Interior angles and if it has more than 3 sides also diagonals
What are the total diagonals in an irregular polygon whose interior angles add up to 1980 degrees showing all work?
Suppose the polygon has V vertices.Then sum of interior angles is (V - 2)*180 degrees = 1980 degrees => V - 2 = 1980/180 = 11 => V = 13 A polygon with V vertices has V*(V-3)/2 = 13*10/2 = 65 diagonals.
If the sum of interior angles a regular polygon is 1080 degrees how many diagonals does this polygon have?
If the polygon has n sides, the sum of its interior angles is 180*(n - 2) degrees. [Whether the polygon is regular or not is irrelevant] So, 180*(n - 2) = 1080 (n - 2) = 6 n = 8 Then number of diagonals = n*(n - 3)/2 = 8*5/2 = 20
How can you determine the sum of the interior angles of a given polygon?
By drawing all the diagonals from one vertex, the polygon is divided up into triangles. The sum of the interior angles of the polygon is equal to the sum of the internal angles in the triangles. With n vertices, each vertex is not directly connected to n-3 other vertices, thus n-3 diagonals can be drawn from a vertex which will create n-2 triangles (each with the sum of their interior angles as 180o); so: sum_of_interior_angles = 180 x (number_of_sides - 2)
Do the diagonals of a rectangle bisect vertex angles?
No, but the diagonals of a square does bisects its interior angles.
What is a polygon with all interior angles congruent?
A polygon with all interior angles congruent Is known as a regular polygon.
What is a polygon with all interior angles called?
If all of its interior angles are equal then it is a regular polygon
What is the size of each individual interior angle of a polygon having 464 diagonals showing key stages of work?
Providing that it is a regular polygon then let its sides be x: So: 0.5*(x2-3x) = 464 diagonals Then: x2-3x-928 = 0 Solving the equation: x = 32 sides Total sum of interior angles: 30*180 = 5400 degrees Each interior angle: (5400+360)/180 = 168.75 degrees
How many sides does a polygon have with angles of 12 degrees?
Any polygon can have two interior angles of 12 degrees. No polygon can have all its interior angles of 12 degrees.
A polygon has interior angles that add up to 360?
Yes. The interior angles of a polygon add up to 360°.
Can you have diagonals in reflex angles?
There's no such thing as the diagonal of an angle anyway. If there's an irregular polygon that has some reflex angles in it, there's no reason the polygon can't have diagonals that terminate in them.
How many side does a regular polygon have with an interior angle of 30?
The smallest regular polygon, an equilateral triangle, has interior angles of 60. A square has interior angles of 90. There can't exist a regular polygon with interior angles of 30.
