Question

Q8)

Part of a regular polygon is shown below. Each interior angle is 150°. (4
150°
Diagram not
accurately drawn
Calculate the number of sides of the polygon.

Answer 1

12 side polygon

Explanation:

Interior angle of n side regular polygon: = ((n-2)x180)/n

((n-2)x180)/n = 150

(n-2)x180 = 150n

180n - 360 = 150n

30n = 360

n = 12

check: (12-2)x180/12 = 150

Answer 2

The polygon has 12 sides (a dodecagon).

Explanation:

Angles in a Regular Polygon

A polygon with n sides has a total sum of internal angles equal to 180°(n-2). This means that each angle (in a regular polygon) measures

`\displaystyle (180(n-2))/(n)`

We are given the interior angle of 150°, thus:

`\displaystyle (180(n-2))/(n)=150`

Multiplying by n:

`\displaystyle 180(n-2)=150n`

Operating

`\displaystyle 180n-360=150n`

Rearranging and simplifying:

`\displaystyle 180n-150n=360`

`\displaystyle 30n=360`

`n=360/30=12`

n = 12

The polygon has 12 sides (a dodecagon).