Answered

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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.

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 class=

Sagot :

Answer:

12 side polygon

Step-by-step 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

elcharly64

Answer:

The polygon has 12 sides (a dodecagon).

Step-by-step 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

[tex]\displaystyle \frac{180(n-2)}{n}[/tex]

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

[tex]\displaystyle \frac{180(n-2)}{n}=150[/tex]

Multiplying by n:

[tex]\displaystyle 180(n-2)=150n[/tex]

Operating

[tex]\displaystyle 180n-360=150n[/tex]

Rearranging and simplifying:

[tex]\displaystyle 180n-150n=360[/tex]

[tex]\displaystyle 30n=360[/tex]

[tex]n=360/30=12[/tex]

n = 12

The polygon has 12 sides (a dodecagon).

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