Question

Sarah assumes that an interior angle of a regular dodecagon is (8x-2)°, then the value of x is​

Answer 1

`x = 19`

Explanation:

Given

Shape: Regular Dodecagon

Interior Angle = 8x - 2

Required

Determine x

The sum of n terms of a regular polygon is:

`Sum=180(n-2)`

Sides of a dodecagon is 12; So, we have:

`Sum=180(12-2)`

`Sum=180(10)`

`Sum=1800`

Each angle is gotten by dividing 1800 by 12

`Angle = (1800)/(12)`

`Angle = 150`

Equate this to 8x - 2:

`8x - 2 = 150`

Solve for x

`8x = 150 + 2`

`8x = 152`

`x = 152/8`

`x = 19`