State true or false:

If the sum of interior angles is double the sum of exterior angles taken in an order of a polygon, then it is a hexagon.

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True

False

answer is A.

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Detailed Solution

Here, we have to state if the sum of interior angles is double the sum of the exterior angles, then that particular polygon is a hexagon or not.
So, the sum of interior angles of a polygon is given by the relation,

(n − 2) × 180 ∘

, where n denotes the number of sides of the polygon.
Now, we know that for a regular hexagon, the number of sides is 6, so the sum of interior angles of the hexagon will be,

(6 − 2) × 180 ∘ = 4 × 180 ∘ = 720 ∘

So, the sum of all the interior angles of the hexagon is found to be

720 ∘

.
Next, we know that the sum of all the exterior angles of a hexagon is

360 ∘

, thus, if we observe, we can say that the sum of all the interior angles of the hexagon is double of the sum of the exterior angles.
Hence, the statement is true.
Hence, the correct option is (1).

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