Question

If the number of diagonals of a convex polygon are 50% more than its sides. Find the sum of all the interior numbers of the polygon

Answer 1

Answer:

720

Step-by-step explanation:

diagonal = n(n-1) / 2 - n

side after 50 percent = 1.5 n

n = 6

Answer 2

CORRECT QUESTION

If the number of diagonals of a convex polygon are 50% more than its sides. Find the sum of all the interior angles of the polygon.

ANSWER

The answer is 720°

GIVEN

The number of diagonals of a convex polygon are 50% more than its sides.

TO FIND

sum of all the interior angles of the polygon.

SOLUTION

We can simply solve the above problem as follows;

We know that,

Let the number of sides of the polygon = n

Number of diagonals = n + 50% of n = 1.5n

Now,

We know that;

n(n-3)/2 = 1.5n

n - 3 = 3

n = 6

Number of sides of polygon = 6

Now,

The sum of interior angles of a polygon = (n-2) × 180°

Therefore,

Sum of interior angles of polygon with 6 sides = (6-2) × 180

= 720°

Hence, The answer is 720°

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