The number of sides are 45
Step-by-step explanation:
The relationship of sides and the sum of interior angles of a convex polygon is given by:
[tex](n-2) * 180 = Sum\ of\ interior\ angles[/tex]
Here n is the number of sides of polygon
Given
Sum of interior angles = 7740°
Putting the values in the equation
[tex](n-2) * 180 = 7740[/tex]
Dividing both sides by 180
[tex]\frac{(n-2)*180}{180} = \frac{7740}{180}\\n-2 = 43[/tex]
Adding 2 on both sides
[tex]n-2+2 = 43+2\\n = 45[/tex]
Hence,
The number of sides are 45
Keywords: Polygon, sum of angles
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Answer: 45 sides
Step-by-step explanation: The sum of the measures of the interior angles of a polygon can be represented by the formula 180 (n - 2). Since the sum of the measures of the interior angles of the given polygon is 7,740°, we can set our formula equal to 7,740 so we have 180 (n - 2) = 7,740.
The n in the formula represents the number of sides of the polygon and the original question is asking for the number of sides of the polygon. So if we solve this equation for n, we will have our answer.
To solve the equation, we start by distributing the 180 through the parentheses on the left side and we have 180n - 360 = 7740 and adding 360 to both sides gives us 180n = 8,100. Dividing both sides of the equation by 180, we find that n = 45.
So if the sum of the measures of the interior angles of a polygon is 7740°, then we know that the polygon has 45 sides.
