Ratio between number of sides of two regular polygons is 2:3 and ratio between degree measure of their interior angles is 3:4. Write the name of these polygons.
(n-2)180/n
To find the name of the two regular polygons, we need to use the information given about the ratios of their number of sides and the ratios of their interior angles' degree measures.
Let's assume that the regular polygons have n sides and m sides, respectively.
According to the given information, the ratio between the number of sides of these polygons is 2:3. Therefore, we can write the equation:
n/m = 2/3
Cross multiplying, we get:
3n = 2m
Similarly, the ratio between the degree measures of their interior angles is 3:4, so we can write the equation:
n/m = 3/4
Cross-multiplying, we get:
4n = 3m
Now we have a system of equations:
3n = 2m
4n = 3m
To solve this system, we can either substitute one equation into the other or use other algebraic techniques.
Let's substitute 3n = 2m into the second equation:
4(2m/3) = 3m
8m/3 = 3m
Multiply both sides of the equation by 3 to eliminate the fraction:
8m = 9m
Subtract 8m from both sides:
0 = m
Since m is equal to 0, the regular polygon with m sides does not exist.
Therefore, there is only one regular polygon in this scenario.
In conclusion, the regular polygon with the ratio of 2:3 between the number of sides and a ratio of 3:4 between the degree measures of the interior angles is simply called a regular polygon with n sides, where n is a positive integer.