Question

What is the sum of the meausures of the interior angles of a polygon which has 20 diagonals​

Answer 1

Ответ: $1080^o$.

Объяснение:

If the number of diagonals is 20, then the number of corners is:

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Formula to find the sum of interior angles of a n-sided polygon:

$S_{n} =(n-2) \cdot 180^o\\\\S_{n} =(8-2) \cdot 180^o=6 \cdot 180^o=1080^o$

Answer 2

To find the sum of the measures of the interior angles of a polygon with 20 diagonals, we can use the formula for the sum of the interior angles of a polygon:

Sum of Interior Angles = (n - 2) * 180 degrees

Where: - "n" is the number of sides of the polygon.

In this case, you want to find the sum of the interior angles of a polygon with 20 diagonals. Diagonals are line segments that connect non-adjacent vertices in a polygon.

We can use a formula to find the number of diagonals in a polygon based on the number of sides (n):

Number of Diagonals = [n(n - 3)] / 2

Now, you know that the number of diagonals is 20. So, we can set up the equation:

20 = [n(n - 3)] / 2

Let's solve for "n" by multiplying both sides by 2:

2 * 20 = n(n - 3)

40 = n^2 - 3n

Now, let's rearrange the equation to form a quadratic equation:

n^2 - 3n - 40 = 0

We can factor this equation:

(n - 8)(n + 5) = 0

Now, we have two possible solutions for "n":

1) n - 8 = 0, which gives n = 8 2) n + 5 = 0, which gives n = -5 (but since the number of sides of a polygon cannot be negative, we discard this solution)

So, the polygon has 8 sides (an octagon). Now we can use the formula for the sum of interior angles:

Sum of Interior Angles = (n - 2) * 180 degrees Sum of Interior Angles = (8 - 2) * 180 degrees Sum of Interior Angles = 6 * 180 degrees Sum of Interior Angles = 1080 degrees

The sum of the measures of the interior angles of the polygon is 1080 degrees.