Question

cuttack is ________mahanadi ​

Answer 1

Answer:

I think the answer is on.

Please mark as the brainliest answer.

Answer 2

Answer:

Required Knowledge

\red{\bigstar}★ Angle sum of a triangle.

The angles of a triangle sum to 180^{\circ}180

∘

.

\red{\bigstar}★ The number of diagonals.

In a regular polygon of nn sides, we can draw (n-3)(n−3) diagonals from a point since we cannot connect adjacent sides or itself to get a diagonal. Also, inside is (n-2)(n−2) triangles.

\red{\bigstar}★ Property of regular polygons.

Every single angle is equal in regular polygons.

\large\underline{\text{Solution}}

Solution

Since there are (n-2)(n−2) triangles, the angle sum of all the triangles is 180^{\circ}\times(n-2)180

∘

×(n−2) .

Then since the regular polygon has nn equal angles, one angle will be \dfrac{180^{\circ}\times(n-2)}{n}

n

180

∘

×(n−2)

.

Now we get the equation.

\implies\dfrac{180^{\circ}\times(n-2)}{n}=144^{\circ}⟹

n

180

∘

×(n−2)

=144

∘

\implies180^{\circ}\times n-360^{\circ}=144^{\circ}\times n⟹180

∘

×n−360

∘

=144

∘

×n

\implies(180^{\circ}-144^{\circ})\times n=360^{\circ}⟹(180

∘

−144

∘

)×n=360

∘

\implies36^{\circ}\times n=360^{\circ}⟹36

∘

×n=360

∘

\implies n=10⟹n=10