phlaym39 wrote:

What is the perimeter of a regular polygon with sides of length 12 cm and internal angles measuring 144° each?

A. 96 cm

B. 108 cm

C. 120 cm

D. 132 cm

E. 144 cm

Sum of ALL sides in an n-sided polygon = (n - 2)(180) degreesSo,

EACH ANGLE in a regular n-sided polygon = (n - 2)(180)/n degrees

We're told that EACH ANGLE is 144°, so we can write: (n - 2)(180)/n = 144

Multiply both sides by n to get: (n - 2)(180) = 144n

Expand left side: 180n - 360 = 144n

Add 360 to both sides: 180n = 144n + 360

Subtract 144n from both sides: 36n = 360

Solve: n =

10This tells us that the polygon has

10 sides

Since each side is the SAME LENGTH in a REGULAR polygon, the perimeter = (

10)(

12 cm) = 120 cm

Answer: C

Cheers,

Brent

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