Question

two angels of a polygon are right angels and the remaining are 120 degree each.find the number of sides in it


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Answer 1

Answer:

uestion

Answers

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Two angles of a polygon are right angles and the remaining angles are 120∘each. Find the number of sides in it.

This question is based on the sum of the internal angles of a polygon. First of all, we assume that the number of sides is n. Now by using the formula of the sum of internal angles of a polygon –

Sum of internal angles of nsided polygon =(n−2)×180∘

By given angles in the question, we make an equation in n and solve it and get the number of sides of a polygon.

Complete step by step answer:

Let us start by understanding what a polygon is. A polygon is a plane figure that is described by a finite number of straight-line segments called edges. There are an equal number of edges and angles in a polygon, and the sum of interior angles and side’s relation is –

S=(n−2)π radian

S=(n−2)×180∘ degree

Let us assume that there are n sides in a polygon. Thus, there are also n internal angles in the polygon.

According to the question, we have the data as below.

Out ofn, two angles are right angle. And the remaining (n−2) angles are 120∘each.

So, we can write that

Sum of internal angles of polygon =(2×90∘)+(n−2)120∘ …(1)

As we know that sum of interior angles of n sided polygon

=(n−2)×180∘ …(2)

Now, by equation (1) and (2), we can equate them as

(n−2)×180∘=(2×90∘)+(n−2)120∘

On dividing by 60∘on both sides, we get

⇒(n−2)×180∘60=(2×90∘)60+(n−2)120∘60

⇒3(n−2)=3+2(n−2)

By subtracting 2(n−2) on both sides, we get

⇒3(n−2)−2(n−2)=3+2(n−2)−2(n−2)

⇒(n−2)=3

By adding 2 on both sides, we get

⇒n−2+2=3+2

⇒n=5

Hence, the number of sides in the polygon is 5.

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Answer 2

Answer:

5

Step-by-step explanation:

Let number of sides of polygon is n.

Two angles of a polygon are right angles and the remaining are 120

o

each

Sum of total angles of a polygon is = 180

o

(n−2)

n= number of sides of polygon

Now,

2×90+n-2×120=180(n-2)

180degree n - 120 degree n = 180+360-240

60n = 300

n=5

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