Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

What is the sum of the interior angle measures in a 20-gon?

1 Answer

Shwetank Mauria

May 16, 2018

Sum of all interior angles of $20$ $20$ -gon is $3240^{\circ}$ $3240^@$

Explanation:

Three things first.

A polygon with $n$ $n$ sides ( $n$ $n$ -gon) has $n$ $n$ interior angles and $n$ $n$ exterior angles.
As sum of each pair of exterior and interior angles is $180^{\circ}$ $180^@$ , sum of all interior and exterior angles is $n \times 180^{\circ}$ $nxx180^@$
Sum of all the exterior angles of any polygon (i.e. irrespective of its number of sides) is always $360^{\circ}$ $360^@$ .

Therefore $20$ $20$ -gon has $20$ $20$ exterior angles whose sum is $360^{\circ}$ $360^@$ .

As such, sum of its all interior and exterior angles is $20 \times 180^{\circ} = 3600^{\circ}$ $20xx180^@=3600^@$

Hence, sum of all interior angles is $3600^{\circ} - 360^{\circ} = 3240^{\circ}$ $3600^@-360^@=3240^@$

Related questions

See all questions in Angles with Triangles and Polygons

Impact of this question

26807 views around the world

You can reuse this answer
Creative Commons License