Answer:
m = 7; n = 12
Explanation:
"a regular n-sided polygon has 5 sides more than a
regular m-sided polygon"
n = m + 5
The sum of the measures of the interior angles is
180(n - 2) for the n-sided polygon and
180(m 2) for the m-sided polygon.
"If the sum of interior angles of the regular
n-sided polygon is twice that of the latter"
180(n - 2) = 2(180)(m - 2)
We have a system of equations with 2 equations.
n = m + 5
180(n - 2) = 2(180)(m - 2)
Simplify the second equation:
n - 2 = 2m - 4
n + 2 = 2m
Substitute m + 5 for n.
m + 5 + 2 = 2m
7 = m
m = 7
n = m + 5 = 7 + 5 = 12
Answer: m = 7; n = 12