Question

The difference between the exterior angle of a regular polygon of N sides and the regular polygon of N+2 sides is 6 find the number of sides.​
pls answer fast

Answer 1

Answer:

enjoy your answer thank please rate

Answer 2

Recall:

Sum of exterior angles of any polygon = 360°

Find the exterior angle of a N side polygon:

$\text{N exterior angles } = 360 ^\circ$

$\text{1 exterior angle } = 360 \div N$

$\text{1 exterior angle } = \dfrac{360}{N}$

Find the exterior angle of a (N+2) side polygon:

$\text{(N + 2) exterior angles } = 360 ^\circ$

$\text{1 exterior angle } = 360 \div (N+2)$

$\text{1 exterior angle } = \dfrac{360}{N+2}$

Solve N:

$\dfrac{360}{N} - \dfrac{360}{N + 2} = 6$

$\dfrac{360(N+ 2) - 360N}{N( N + 2)} = 6$

$\dfrac{360N + 720 - 360N}{N(N + 2)} = 6$

$\dfrac{720}{N(N + 2)} = 6$

$720 = 6N(N + 2)$

$720 = 6N^2 + 12N$

$6N^2+12N-720 = 0$

$6(n + 12)(n - 10) = 0$

$n = 10 \text{ or } n = -12 \text {\text{ (Rejected)}}$

Find the number of sides:

$\text{Number of sides of one polygon} = N$

$\text{Number of sides of one polygon} = 10$

$\text{Number of sides of the other polygon} = N + 2$

$\text{Number of sides of the other polygon} = 10 + 2$

$\text{Number of sides of the other polygon} = 12$

Answers: They are 10-sided and 12-sided polygon.