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Ahat [919]
3 years ago
10

Each interior angle of a regular n-sided polygon is 150 degrees. How many sides does the polygon have?

Mathematics
1 answer:
notsponge [240]3 years ago
5 0
The sum of the interior angles of the polygon = (n - 2) x 180 .

(n - 2) x 180 = (n x 150)

180n - 360 = 150n

Add 360 to each side:

180n = 150n + 360

Subtract 150n from each side:

30n = 360

Divide each side by 30 :

<u>n = 12</u>
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Nimfa-mama [501]

The question was incomplete. Below you will find the missing content.

In the figure below, BL, AM, and CK are medians of △ABC. If KC = 108 and OC = 2n + 10, then n=

The picture is attached below.

The value of n is 31.

The median is the line connecting the vertex and its midpoint on the opposite side of the triangle.

The intersection of all 3 medians of the triangle is called the centroid.

As we know centroid divides the median in the ratio of 2:1.

In the given picture,

Medians of triangle △ABC are AM, BL, and CK.

So the centroid of the triangle is O.

Given that KC= 108

As the centroid O divides the line KC in 2:1.

Let OC=2x

KO= X

As KC= KO+OC

⇒ 108= x+2x

⇒ 3x=108

⇒ x=108/3

⇒ x=36

Then OC= 2x= 2*36= 72

As given in the question OC= 2n+10

putting the value of OC in above equation

⇒ 72= 2n+10

⇒ 2n= 72-10

⇒ 2n=62

⇒ n=62/2

⇒n=31

Therefore the value of n is 31.

Learn more about the median of the triangle

here: brainly.com/question/2264495

#SPJ10

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