Tag: circumscribing and inscribing a circle on a regular hexagon

Questions Related to circumscribing and inscribing a circle on a regular hexagon

The sum of all the angles of a pentagon are

maths construction circumscribing and inscribing a circle on a regular hexagon construction of tangent to a circle construction of tangents

  1. $360^\circ$

  2. $540^\circ$

  3. $720^\circ$

  4. none of these

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Correct Option: B
Explanation:

Pentagon is a five sided polygon.

The sum of the interior angles of the pentagon is the sum of interior angles of the three triangles.The sum of interior angles of the three triangles is 180 degree.so the sum of interior angles of the pentagon is 3 times 180 degree which is 540 degree.

Inscribe a regular pentagon in a circle of radius $3\ cm$. The interior angles of the pentagon are:

maths construction circumscribing and inscribing a circle on a regular hexagon construction of tangent to a circle construction of tangents

  1. $54^\circ$

  2. $60^\circ$

  3. $162^\circ$

  4. $108^\circ$

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Correct Option: D
Explanation:

We know that internal angle of regular pentagon is $\cfrac{(n-2)}{n}180^{\circ}$ where n = number of sides.

Here, n = 5.
So, interior angle is $\cfrac{(5-2)}{5}180^{\circ} = 108^{\circ}$

So correct answer is option D