Which of the following regular polygons has sum of all the interior angles as 720-Regular hexagon-Pentagon-Equilateral triangle-Rhombus-

The correct option is A Regular hexagon Sum of interior angles of a regular polygon = (n 2) × 180^∘ where n being the number of sides in a regular polygon. ...

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Standard VII

Mathematics

Interior Angles of a Polygon

Which of the ...

Question

Which of the following regular polygons has sum of all the interior angles as 720°?

Pentagon

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Equilateral triangle

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Rhombus

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Regular hexagon

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Solution

The correct option is D
Regular hexagon

Sum of interior angles of a regular polygon = $(n - 2) \times 180^{\circ}$
where n being the number of sides in a regular polygon.

$720^{\circ} = (n - 2) \times 180^{\circ}$
$\Rightarrow 4 = n - 2$
$\Rightarrow n = 6$

Hence, the sum of all interior angles of a regular hexagon is $720^{\circ}$ .

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Which of the following regular polygons has sum of all the interior angles as 720°?

The correct option is D Regular hexagon Sum of interior angles of a regular polygon = (n−2)×180∘ where n being the number of sides in a regular polygon. 720∘=(n−2)×180∘ ⇒ 4=n−2 ⇒ n=6 Hence, the sum of all interior angles of a regular hexagon is 720∘.