Tag: circumscribing and inscribing a circle on a regular hexagon

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

The sum of all the angles of a pentagon are

  1. $360^\circ$
  2. $540^\circ$
  3. $720^\circ$

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. $54^\circ$
  2. $60^\circ$
  3. $162^\circ$
  4. $108^\circ$
Reveal answer Fill a bubble to check yourself
D Correct answer
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