Question

Can a polygon have the sum of its interior angles as: (i) 2160º (ii) 2400º

Answer 1

Answer:

yes

Step-by-step explanation:

solve the equation with the help of formula

Answer 2

Question :- Can a regular polygon have the sum of its interior angles as: (i) 2160º (ii) 2400º ?

Solution :-

we know that,

• sum of interior angles of a regular with n sides is = (n - 2) * 180° , where n is a natural number greater than 2 .

so,

→ (n - 2) * 180° = 2160°

dividing both sides by 180°

→ (n - 2) = 12

→ n = 12 + 2

→ n = 14 .

therefore, we can conclude that, 2160° can be the sum of interior angles of a regular polygon.

also,

→ (n - 2) * 180° = 240°

dividing both sides by 60°

→ (n - 2) * 3 = 4

→ 3n - 6 = 4

→ 3n = 4 + 6

→ 3n = 10

→ n = (10/3) ≠ Natural Number.

therefore, we can conclude that, 2400° can not be the sum of interior angles of a regular polygon.

Learn more :-

In ABC, AD is angle bisector,

angle BAC = 111 and AB+BD=AC find the value of angle ACB=?

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